FAD1022: Rapid-Fire Drill Pack — CQ3 AC Analysis

Objective: Achieve mechanical fluency in AC circuit calculations: reactance, impedance, phasors, resonance, and power.
Target: 45–60 seconds per problem. If you stall >3 minutes, skip and mark it.
Total problems: 70
Estimated time: 60–80 minutes

Cheat Sheet (Memorize First)

Symbol Formula When to Use
$V_{\text{rms}}$ $\displaystyle \frac{V_{\max}}{\sqrt{2}} \approx 0.707,V_{\max}$ Converting peak ↔ RMS (sinusoid only)
$I_{\text{rms}}$ $\displaystyle \frac{I_{\max}}{\sqrt{2}}$ Converting peak ↔ RMS current
$\omega$ $2\pi f = \dfrac{2\pi}{T}$ Angular frequency (rad/s)
$X_L$ $2\pi f L = \omega L$ Inductive reactance (Ω)
$X_C$ $\dfrac{1}{2\pi f C} = \dfrac{1}{\omega C}$ Capacitive reactance (Ω)
$Z$ (RLC) $\sqrt{R^2 + (X_L - X_C)^2}$ Total impedance of series RLC
$Z$ (RL) $\sqrt{R^2 + X_L^2}$ Series RL impedance
$Z$ (RC) $\sqrt{R^2 + X_C^2}$ Series RC impedance
$\tan\phi$ $\dfrac{X_L - X_C}{R}$ Phase angle (positive = inductive, voltage leads)
$f_0$ $\dfrac{1}{2\pi\sqrt{LC}}$ Resonant frequency
$P_{\text{avg}}$ $I_{\text{rms}}^2 R = V_{\text{rms}}I_{\text{rms}}\cos\phi$ Real / average power (W)
$Q$ $I_{\text{rms}}^2(X_L - X_C)$ Reactive power (VAR)
$S$ $V_{\text{rms}}I_{\text{rms}} = \sqrt{P^2 + Q^2}$ Apparent power (VA)
$\text{PF}$ $\cos\phi = \dfrac{R}{Z} = \dfrac{P}{S}$ Power factor (0–1)
$V_T$ (RLC) $\sqrt{V_R^2 + (V_L - V_C)^2}$ Total voltage phasor sum

CIVIL Mnemonic

  • Capacitor: I leads V by $90°$
  • L inductor: V leads I by $90°$

Common Traps

  1. Adding $V_R$, $V_L$, $V_C$ algebraically instead of phasor (Pythagorean) sum.
  2. Mixing peak and RMS in the same equation.
  3. Forgetting that $X_C \propto 1/f$ while $X_L \propto f$.
  4. Phase angle sign: positive = inductive (voltage leads), negative = capacitive (current leads).
  5. At resonance $Z = R$ (minimum), $I$ is maximum, $\phi = 0°$, $\text{PF} = 1$.

Part A: AC Fundamentals & RMS

Target: 30–45 seconds per problem.

Set A1 — Waveform Parameters (5 problems)

Write the equation, then state the requested quantity.

  1. $I(t) = 6\sin(100\pi t)\ \text{A}$. Find the peak current, RMS current, frequency, and period.
  2. A household outlet is $240\ \text{V RMS}$, $50\ \text{Hz}$. Write the instantaneous voltage equation $V(t)$ in sine form.
  3. $V(t) = 170\sin(120\pi t)\ \text{V}$. Determine $V_{\text{rms}}$ and the frequency.
  4. An AC current has a period of $0.04\ \text{s}$ and a peak value of $2.5\ \text{A}$. Write $I(t)$.
  5. A signal has $f = 1.0\ \text{kHz}$ and $V_{\max} = 10\ \text{V}$. Calculate $\omega$ and $V_{\text{rms}}$.

Score: ___/5

Set A2 — Instantaneous Values & Phase (5 problems)

  1. For $V(t) = 325\sin(100\pi t)\ \text{V}$, calculate the instantaneous voltage at $t = 5.0\ \text{ms}$.
  2. A current is described by $I(t) = 4\sin(200\pi t + \pi/3)\ \text{A}$. What is the phase angle, and does it lead or lag the reference $\sin(200\pi t)$?
  3. $V(t) = 15\sin(\omega t - \pi/4)\ \text{V}$. What is the voltage at $t = 0$?
  4. In a circuit, current lags voltage by $30°$. If $V(t) = V_0\sin(\omega t)$, write $I(t)$.
  5. Rewrite $I(t) = 3\cos(\omega t)$ as a sine function with a phase angle.

Score: ___/5

Part B: Reactance & Pure Circuits

Target: 45–60 seconds per problem.

Set B1 — Reactance Calculations (6 problems)

  1. An inductor $L = 0.50\ \text{H}$ is connected to a $50\ \text{Hz}$ source. Calculate $X_L$.
  2. A capacitor $C = 10\ \mu\text{F}$ is connected to a $50\ \text{Hz}$ source. Calculate $X_C$.
  3. An inductor has $X_L = 200\ \Omega$ at $100\ \text{Hz}$. Find its inductance.
  4. A capacitor has $X_C = 500\ \Omega$ at $1.0\ \text{kHz}$. Find its capacitance.
  5. An inductor $L = 20\ \text{mH}$ operates at $\omega = 5.0\times10^3\ \text{rad/s}$. Find $X_L$.
  6. A capacitor $C = 0.10\ \mu\text{F}$ operates at $\omega = 1.0\times10^4\ \text{rad/s}$. Find $X_C$.

Score: ___/6

Set B2 — Pure Circuit Behavior (6 problems)

  1. In a pure capacitive circuit, $V(t) = V_0\sin(\omega t)$. Write the current equation $I(t)$ and state the phase relationship.
  2. In a pure inductive circuit, $I(t) = I_0\sin(\omega t)$. Write the voltage equation $V(t)$ and state the phase relationship.
  3. A pure resistor has $V_{\text{rms}} = 12\ \text{V}$ and $I_{\text{rms}} = 3.0\ \text{A}$. What is its impedance?
  4. A pure capacitor has $V_{\text{rms}} = 24\ \text{V}$, $I_{\text{rms}} = 6.0\ \text{mA}$, and $f = 50\ \text{Hz}$. Determine the capacitance.
  5. A pure inductor has $V_0 = 50\ \text{V}$, $I_0 = 2.5\ \text{A}$, and $f = 60\ \text{Hz}$. Determine the inductance.
  6. In a pure inductive circuit, does current lead or lag voltage? By what angle?

Score: ___/6

Part C: Series RL & RC Circuits

Target: 60–90 seconds per problem.

Set C1 — RL Series Circuits (6 problems)

  1. A $30\ \Omega$ resistor is in series with a $0.20\ \text{H}$ inductor across a $50\ \text{Hz}$ source. Calculate $X_L$ and the total impedance $Z$.
  2. A series RL circuit has $R = 40\ \Omega$ and $X_L = 30\ \Omega$, driven by $V_{\text{rms}} = 100\ \text{V}$. Find $I_{\text{rms}}$, $V_R$, and $V_L$.
  3. A $100\ \Omega$ resistor and a $150\ \text{mH}$ inductor are connected to a $230\ \text{V}$, $60\ \text{Hz}$ supply. Calculate the phase angle $\theta$.
  4. In an RL series circuit, the voltages measured are $V_R = 60\ \text{V}$ and $V_L = 80\ \text{V}$. What is the total supply voltage $V_T$?
  5. A series RL circuit with $R = 50\ \Omega$ draws $2.0\ \text{A}$ from a $120\ \text{V}$, $50\ \text{Hz}$ source. Find the inductance $L$.
  6. An RL circuit has $Z = 130\ \Omega$, $R = 50\ \Omega$, and $f = 60\ \text{Hz}$. Determine the inductance.

Score: ___/6

Set C2 — RC Series Circuits (6 problems)

  1. A $100\ \Omega$ resistor is in series with a $15\ \mu\text{F}$ capacitor across a $60\ \text{Hz}$ source. Calculate $X_C$ and $Z$.
  2. A series RC circuit has $R = 200\ \Omega$ and $X_C = 150\ \Omega$, driven by $V_{\text{rms}} = 50\ \text{V}$. Find $I_{\text{rms}}$, $V_R$, and $V_C$.
  3. In an RC series circuit, $V_R = 90\ \text{V}$ and $V_C = 120\ \text{V}$. What is the total supply voltage $V_T$?
  4. A $1.0\ \text{k}\Omega$ resistor and a $0.10\ \mu\text{F}$ capacitor are driven at $\omega = 1.0\times10^4\ \text{rad/s}$. Find $Z$ and the phase angle.
  5. A series RC circuit has a phase angle of $-60°$ and $R = 100\ \Omega$ at $50\ \text{Hz}$. Find the capacitance.
  6. A $50\ \Omega$ resistor and a $50\ \mu\text{F}$ capacitor are connected to a $230\ \text{V}$, $60\ \text{Hz}$ source. Calculate $I_{\text{rms}}$ and the power factor.

Score: ___/6

Part D: Series RLC & Resonance

Target: 60–90 seconds per problem.

Set D1 — RLC Impedance & Phase (5 problems)

  1. A series RLC circuit has $R = 40\ \Omega$, $X_L = 90\ \Omega$, and $X_C = 30\ \Omega$. Calculate $Z$ and the phase angle $\theta$.
  2. A series RLC circuit has $R = 100\ \Omega$, $X_L = 50\ \Omega$, and $X_C = 120\ \Omega$. Calculate $Z$ and $\theta$.
  3. A series RLC circuit has $R = 75\ \Omega$, $X_C = 90\ \Omega$, $X_L = 165\ \Omega$, and is driven by $120\ \text{V}$. Calculate the circuit current.
  4. In a series RLC circuit, $V_R = 80\ \text{V}$, $V_L = 150\ \text{V}$, and $V_C = 70\ \text{V}$. Find $V_T$ and the phase angle.
  5. A series RLC circuit has $R = 50\ \Omega$, $L = 0.10\ \text{H}$, $C = 10\ \mu\text{F}$, and $\omega = 1000\ \text{rad/s}$. Find $Z$, $\theta$, and identify the leading signal (if any).

Score: ___/5

Set D2 — Resonance (5 problems)

  1. An inductor $L = 0.80\ \text{H}$ and a capacitor $C = 5.0\ \mu\text{F}$ form a series RLC circuit. Calculate the resonance frequency $f_0$.
  2. A series RLC circuit has $R = 10\ \Omega$, $L = 0.50\ \text{H}$, $C = 20\ \mu\text{F}$, and is driven by $V_{\text{rms}} = 100\ \text{V}$. At resonance, find $I_{\text{rms}}$, $Z$, $\theta$, and the power factor.
  3. Find the capacitance required for resonance at $f_0 = 1000\ \text{Hz}$ when $L = 0.10\ \text{H}$.
  4. At resonance in a series RLC circuit, $X_L = X_C = 200\ \Omega$, $R = 50\ \Omega$, and $V_{\text{rms}} = 120\ \text{V}$. Calculate the RMS voltages across the inductor and the capacitor.
  5. A series RLC circuit has $R = 100\ \Omega$, $L = 0.20\ \text{H}$, $C = 20\ \mu\text{F}$. The RMS voltage across the inductor is $50\ \text{V}$ and across the capacitor is $200\ \text{V}$. Determine the operating frequency.

Score: ___/5

Set D3 — Frequency Response & Behavior (4 problems)

  1. The inductive and capacitive reactances of a circuit are equal at $2.0\ \text{kHz}$. What is the ratio $X_C / X_L$ at $200\ \text{Hz}$?
  2. Describe how the impedance of a series RLC circuit behaves as the frequency increases from zero to a very high value.
  3. A $2.0\ \text{H}$ inductor is connected in series with an unknown capacitor to a $240\ \text{V}$, $50\ \text{Hz}$ supply. What value of $C$ makes the current in phase with the voltage?
  4. A series RLC circuit has $R = 300\ \Omega$, $L = 0.80\ \text{H}$, and $C = 5.0\ \mu\text{F}$. Calculate the resonance frequency. At $f = 50\ \text{Hz}$, find the impedance and phase angle.

Score: ___/4

Part E: Power & Power Factor

Target: 60–90 seconds per problem.

Set E1 — Basic Power Calculations (6 problems)

  1. A resistor $R = 60\ \Omega$ is connected to an AC source with $V_{\text{rms}} = 120\ \text{V}$. Calculate the average power dissipated.
  2. A series RL circuit has $R = 30\ \Omega$ and $X_L = 40\ \Omega$, driven by $V_{\text{rms}} = 100\ \text{V}$. Calculate $P_{\text{avg}}$, reactive power $Q$, apparent power $S$, and the power factor.
  3. A series RLC circuit has $R = 12\ \Omega$, $X_L = 30\ \Omega$, $X_C = 20\ \Omega$, and $V_R = 145\ \text{V}$. Calculate $P_{\text{avg}}$, $Q$, and $S$.
  4. A series RC circuit has $R = 150\ \Omega$ and $X_C = 150\ \Omega$, connected to a $120\ \text{V}$ source. Calculate the apparent power $S$.
  5. An AC load draws $I_{\text{rms}} = 5.0\ \text{A}$ from a $230\ \text{V}$ supply with a power factor of $0.85$. Find the average power.
  6. A circuit consumes $P_{\text{avg}} = 800\ \text{W}$ from a $230\ \text{V}$ supply with $\text{PF} = 0.85$. Find $I_{\text{rms}}$ and the apparent power $S$.

Score: ___/6

Set E2 — Power Triangle & Factor (6 problems)

  1. A load has $P_{\text{avg}} = 500\ \text{W}$ and reactive power $Q = 300\ \text{VAR}$. Find the apparent power $S$ and the power factor.
  2. An AC source delivers apparent power $S = 1000\ \text{VA}$ to a load with $\text{PF} = 0.75$ lagging. Find the real power $P$ and reactive power $Q$.
  3. A series RL circuit has $R = 50\ \Omega$ and $L = 150\ \text{mH}$, connected to $230\ \text{V}$, $60\ \text{Hz}$. Calculate the power factor.
  4. An industrial load draws $P = 10\ \text{kW}$ with $Q = 5\ \text{kVAR}$ inductive. Find $S$ and the phase angle.
  5. A series RLC circuit has $R = 200\ \Omega$, $L = 300\ \text{mH}$, $C = 200\ \mu\text{F}$, and is driven by $120\ \text{V}$ at $50\ \text{Hz}$. Calculate the power factor.
  6. A motor draws $8.0\ \text{A}$ at $230\ \text{V}$ with a power factor of $0.80$ lagging. What are its apparent power and real power?

Score: ___/6

Part F: Mixed & Reverse Engineering

Target: 90–120 seconds per problem.

Set F1 — Black Box & Partial Information (5 problems)

  1. A black box contains an unknown resistor and inductor in series. At $50\ \text{Hz}$ and $100\ \text{V}$, the current is $2.0\ \text{A}$ and the voltage across the resistor is $80\ \text{V}$. Find $R$ and $L$.
  2. A black box contains an unknown resistor and capacitor in series. At $50\ \text{Hz}$ and $120\ \text{V}$, the current is $0.50\ \text{A}$ and the phase angle is $-60°$. Find $R$ and $C$.
  3. A series RLC circuit has $V_R = 40\ \text{V}$, $V_L = 70\ \text{V}$, $V_C = 100\ \text{V}$, and $R = 20\ \Omega$. Find the current, the total voltage, and state whether the circuit is more inductive or capacitive.
  4. A coil (resistance + inductance in series) has an impedance of $50\ \Omega$ at $50\ \text{Hz}$ and $80\ \Omega$ at $100\ \text{Hz}$. Determine $R$ and $L$.
  5. A series RLC circuit is at resonance. The current is $5.0\ \text{A}$, $V_L = 500\ \text{V}$, $V_C = 500\ \text{V}$, and $R = 20\ \Omega$. What is the supply RMS voltage?

Score: ___/5

Set F2 — Design & Challenge Problems (5 problems)

  1. Design a series RL circuit that has a phase angle magnitude of $30°$ and impedance $Z = 100\ \Omega$ at $60\ \text{Hz}$. Find the required $R$ and $L$.
  2. You need a resonant frequency of $1.0\ \text{MHz}$ using an inductor of $L = 10\ \mu\text{H}$. What capacitance $C$ is required?
  3. A series RC circuit must draw $2.0\ \text{A}$ from a $120\ \text{V}$ source with a power factor of $0.60$. Find $R$ and $X_C$.
  4. A $100\ \text{W}$ incandescent bulb operates at $230\ \text{V RMS}$. Calculate its peak current.
  5. A series RLC circuit has $R = 100\ \Omega$, $L = 0.50\ \text{H}$, and $C = 20\ \mu\text{F}$. At resonance, what is the current if $V_{\text{rms}} = 50\ \text{V}$? At what frequency does this occur?

Score: ___/5

Final Scorecard

Part Sets Problems Raw Score
A — AC Fundamentals & RMS A1, A2 10 ___/10
B — Reactance & Pure Circuits B1, B2 12 ___/12
C — Series RL & RC Circuits C1, C2 12 ___/12
D — Series RLC & Resonance D1, D2, D3 14 ___/14
E — Power & Power Factor E1, E2 12 ___/12
F — Mixed & Reverse Engineering F1, F2 10 ___/10
TOTAL 70 ___/70

Proficiency Benchmarks

  • 49/70 (70%) — Proficient. You can handle standard exam problems; review missed sets.
  • 60/70 (85%) — Solid. Fast and accurate on most archetypes.
  • 65/70 (93%) — Exam-ready. Any mistake is a careless slip or a rare edge case.

Speed Benchmarks

  • <55 minutes: Excellent mechanical fluency.
  • 55–75 minutes: Good. Review the specific sets you scored lowest on.
  • >75 minutes: Drill the sets you scored lowest on again tomorrow before attempting new problems.

Error Log Template

After grading, list every wrong problem number with a one-word reason:

Problem Reason
e.g. 4 forgot √2
2 Did not convert V_rms

Re-solve all wrong problems immediately with notes, then again in 24 hours without notes.

Answer Key

Set A1

  1. $I_{\max} = 6.0\ \text{A}$; $I_{\text{rms}} = 4.24\ \text{A}$; $f = 50\ \text{Hz}$; $T = 0.020\ \text{s}$
  2. $V(t) = 339\sin(100\pi t)\ \text{V}$
  3. $V_{\text{rms}} = 120\ \text{V}$; $f = 60\ \text{Hz}$
  4. $I(t) = 2.5\sin(50\pi t)\ \text{A}$
  5. $\omega = 6.28\times10^3\ \text{rad/s}$; $V_{\text{rms}} = 7.07\ \text{V}$

Set A2

  1. $V = 325\sin(0.5\pi) = 325\ \text{V}$
  2. $\phi = +\pi/3$; leads the reference
  3. $V(0) = 15\sin(-\pi/4) = -10.6\ \text{V}$
  4. $I(t) = I_0\sin(\omega t - 30°)$
  5. $I(t) = 3\sin(\omega t + \pi/2)$

Set B1

  1. $X_L = 157\ \Omega$
  2. $X_C = 318\ \Omega$
  3. $L = 0.318\ \text{H}$
  4. $C = 0.318\ \mu\text{F}$
  5. $X_L = 100\ \Omega$
  6. $X_C = 1000\ \Omega$

Set B2

  1. $I(t) = I_0\sin(\omega t + \pi/2)$; current leads voltage by $90°$
  2. $V(t) = V_0\sin(\omega t + \pi/2)$; voltage leads current by $90°$
  3. $Z = 4.0\ \Omega$
  4. $X_C = 4.0\ \text{k}\Omega$; $C = 0.796\ \mu\text{F}$
  5. $X_L = 20\ \Omega$; $L = 53.1\ \text{mH}$
  6. Current lags voltage by $90°$

Set C1

  1. $X_L = 62.8\ \Omega$; $Z = 69.5\ \Omega$
  2. $Z = 50\ \Omega$; $I_{\text{rms}} = 2.0\ \text{A}$; $V_R = 80\ \text{V}$; $V_L = 60\ \text{V}$
  3. $X_L = 56.5\ \Omega$; $\theta = 29.4°$
  4. $V_T = 100\ \text{V}$
  5. $Z = 60\ \Omega$; $X_L = 33.2\ \Omega$; $L = 106\ \text{mH}$
  6. $X_L = 120\ \Omega$; $L = 318\ \text{mH}$

Set C2

  1. $X_C = 177\ \Omega$; $Z = 203\ \Omega$
  2. $Z = 250\ \Omega$; $I_{\text{rms}} = 0.20\ \text{A}$; $V_R = 40\ \text{V}$; $V_C = 30\ \text{V}$
  3. $V_T = 150\ \text{V}$
  4. $X_C = 1000\ \Omega$; $Z = 1.41\ \text{k}\Omega$; $\theta = -45°$
  5. $X_C = 173\ \Omega$; $C = 18.4\ \mu\text{F}$
  6. $X_C = 53.1\ \Omega$; $Z = 72.9\ \Omega$; $I_{\text{rms}} = 3.16\ \text{A}$; $\text{PF} = 0.686$

Set D1

  1. $Z = 50\ \Omega$; $\theta = +56.3°$ (inductive)
  2. $Z = 112\ \Omega$; $\theta = -35.0°$ (capacitive)
  3. $Z = 106\ \Omega$; $I = 1.13\ \text{A}$
  4. $V_T = 100\ \text{V}$; $\theta = +38.7°$ (inductive)
  5. $X_L = 100\ \Omega$; $X_C = 100\ \Omega$; $Z = 50\ \Omega$; $\theta = 0°$; voltage and current are in phase (resonance)

Set D2

  1. $f_0 = 79.6\ \text{Hz}$
  2. $Z = 10\ \Omega$; $I_{\text{rms}} = 10\ \text{A}$; $\theta = 0°$; $\text{PF} = 1$
  3. $C = 0.253\ \mu\text{F}$
  4. $I_{\text{rms}} = 2.4\ \text{A}$; $V_L = V_C = 480\ \text{V}$
  5. $X_L = 50\ \Omega$; $f = 39.8\ \text{Hz}$

Set D3

  1. $100$
  2. $Z$ starts large (capacitive), decreases to a minimum at $f_0$ ($Z=R$), then increases again (inductive).
  3. $X_L = 628\ \Omega$; $C = 5.07\ \mu\text{F}$
  4. $f_0 = 79.6\ \text{Hz}$; at $50\ \text{Hz}$: $X_L = 251\ \Omega$, $X_C = 637\ \Omega$, $Z = 488\ \Omega$, $\theta = -52.1°$

Set E1

  1. $I_{\text{rms}} = 2.0\ \text{A}$; $P_{\text{avg}} = 240\ \text{W}$
  2. $Z = 50\ \Omega$; $I = 2.0\ \text{A}$; $P = 120\ \text{W}$; $Q = 160\ \text{VAR}$; $S = 200\ \text{VA}$; $\text{PF} = 0.60$
  3. $I = 12.08\ \text{A}$; $P = 1752\ \text{W}$; $Q = 1459\ \text{VAR}$; $S = 2279\ \text{VA}$
  4. $Z = 212\ \Omega$; $I = 0.566\ \text{A}$; $S = 67.9\ \text{VA}$
  5. $P = 977.5\ \text{W}$
  6. $S = 941\ \text{VA}$; $I = 4.09\ \text{A}$

Set E2

  1. $S = 583\ \text{VA}$; $\text{PF} = 0.857$
  2. $P = 750\ \text{W}$; $Q = 661\ \text{VAR}$
  3. $X_L = 56.5\ \Omega$; $Z = 75.5\ \Omega$; $\text{PF} = 0.662$
  4. $S = 11.2\ \text{kVA}$; $\theta = 26.6°$
  5. $X_L = 94.2\ \Omega$; $X_C = 15.9\ \Omega$; $Z = 215\ \Omega$; $\text{PF} = 0.931$
  6. $S = 1840\ \text{VA}$; $P = 1472\ \text{W}$

Set F1

  1. $R = 40\ \Omega$; $X_L = 30\ \Omega$; $L = 95.5\ \text{mH}$
  2. $Z = 240\ \Omega$; $R = 120\ \Omega$; $X_C = 208\ \Omega$; $C = 15.3\ \mu\text{F}$
  3. $I = 2.0\ \text{A}$; $V_T = 50\ \text{V}$; capacitive ($V_C > V_L$)
  4. $R = 34.6\ \Omega$; $L = 115\ \text{mH}$
  5. $V_{\text{rms}} = I_{\text{rms}}R = 100\ \text{V}$ (Trap: do not add $V_L + V_C$ to the supply voltage)

Set F2

  1. $R = 86.6\ \Omega$; $X_L = 50\ \Omega$; $L = 133\ \text{mH}$
  2. $C = 2.53\ \text{nF}$
  3. $Z = 60\ \Omega$; $R = 36\ \Omega$; $X_C = 48\ \Omega$
  4. $I_{\text{rms}} = 0.435\ \text{A}$; $I_{\max} = 0.615\ \text{A}$
  5. $f_0 = 50.3\ \text{Hz}$; $I = 0.50\ \text{A}$

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