Ammeter and Voltmeter

Ammeters and voltmeters are the two most fundamental instruments for electrical measurement. Understanding their construction, operation, and proper usage is essential for circuit analysis and experimentation.

Overview

flowchart TD
    A[Electrical Meters] --> B[Ammeter]
    A --> C[Voltmeter]
    
    B --> B1[Measures Current]
    B --> B2[Series Connection]
    B --> B3[Low Resistance]
    
    C --> C1[Measures Voltage]
    C --> C2[Parallel Connection]
    C --> C3[High Resistance]
    
    style B fill:#e1f5e1
    style C fill:#fff9c4

Ammeter

Purpose

Measures electric current (I) flowing through a circuit — the rate of flow of electric charge.

Symbol and Unit

  • Symbol: A
  • Unit: Ampere (A)
  • Subunits: milliampere (mA), microampere (μA)

Connection Method

flowchart LR
    A[V_source] --- B[Ammeter<br/>Series] --- C[Load<br/>R_L] --- D[GND]
    
    style B fill:#fff9c4

Ammeters are always connected in SERIES with the circuit.

Ideal vs Real Ammeter

Property Ideal Ammeter Real Ammeter
Internal resistance $R_{int} = 0$ Small but non-zero
Voltage drop $V = 0$ Small voltage drop
Effect on circuit None Slightly reduces current

Construction from Galvanometer

A basic ammeter is a galvanometer with a shunt resistor in parallel:

flowchart LR
    A[Current In] --- B[Galvanometer<br/>R_g] --- C[Current Out]
    A --- D[Shunt<br/>R_s] --- C
    
    style B fill:#fff9c4
    style D fill:#e1f5e1

Principle: Most current flows through the low-resistance shunt; only a small fraction flows through the sensitive galvanometer.

Shunt resistance formula:

$$R_s = \frac{R_g}{n - 1}$$

Where $n$ is the multiplication factor (full-scale current / galvanometer current).

Loading Effect

When an ammeter is inserted:

$$R_{total} = R_{circuit} + R_{ammeter}$$

$$I_{measured} = \frac{V}{R_{circuit} + R_{ammeter}} < I_{true}$$

To minimize loading: Use an ammeter with $R_{ammeter} \ll R_{circuit}$

Voltmeter

Purpose

Measures potential difference (voltage, V) between two points — the energy per unit charge.

Symbol and Unit

  • Symbol: V
  • Unit: Volt (V)
  • Subunits: millivolt (mV), kilovolt (kV)

Connection Method

flowchart LR
    A[V_source] --- B[R1] --- C[V_test] --- D[R2] --- E[GND]
    C --- F[Voltmeter<br/>Parallel] --- E
    
    style F fill:#fff9c4

Voltmeters are always connected in PARALLEL across the component.

Ideal vs Real Voltmeter

Property Ideal Voltmeter Real Voltmeter
Internal resistance $R_{int} = \infty$ High but finite
Current drawn $I = 0$ Small current
Effect on circuit None Slightly reduces voltage

Construction from Galvanometer

A basic voltmeter is a galvanometer with a series multiplier resistor:

flowchart LR
    A[Point 1] --- B[Multiplier<br/>R_m] --- C[Galvanometer<br/>R_g] --- D[Point 2]
    
    style C fill:#fff9c4
    style B fill:#e1f5e1

Principle: The high resistance limits current through the galvanometer; deflection is proportional to voltage.

Multiplier resistance formula:

$$R_m = R_g(n - 1)$$

Where $n$ is the multiplication factor (full-scale voltage / galvanometer voltage).

Loading Effect

When a voltmeter is connected:

$$R_{parallel} = \frac{R_{circuit} \cdot R_{voltmeter}}{R_{circuit} + R_{voltmeter}} < R_{circuit}$$

$$V_{measured} = V_{true} \times \frac{R_{parallel}}{R_{circuit}} < V_{true}$$

To minimize loading: Use a voltmeter with $R_{voltmeter} \gg R_{circuit}$

Comparison Table

Feature Ammeter Voltmeter
Measures Current (I) Voltage (V)
Connection Series Parallel
Ideal resistance Zero Infinite
Real resistance Very low (mΩ to Ω) Very high (kΩ to MΩ)
Loading effect Reduces current Reduces voltage
Construction Galvanometer + shunt Galvanometer + multiplier

The Galvanometer

What is a Galvanometer?

A galvanometer is a sensitive electromechanical instrument that detects small electric currents.

Construction

flowchart TB
    A[Current enters] --> B[Coil of wire]
    B --> C[Coil suspended in<br/>magnetic field]
    C --> D[Pointer attached<br/>to coil]
    D --> E[Scale shows<br/>deflection]
    
    style C fill:#fff9c4
    style E fill:#e1f5e1

Characteristics

Property Typical Value
Full-scale current Microamperes (μA) to milliamperes (mA)
Coil resistance Tens to hundreds of ohms
Sensitivity Very high — detects tiny currents
Direction Can detect current direction (center-zero type)

Uses

  1. As a detector — Null detection in bridge circuits
  2. As a base meter — Converted to ammeters and voltmeters
  3. As a galvanometer — Measuring small currents directly

Practical Usage Guidelines

Using an Ammeter

flowchart TD
    A[Select appropriate<br/>current range] --> B[Connect in series]
    B --> C[Observe polarity<br/>+ to +, - to -]
    C --> D[Start with highest<br/>range if uncertain]
    D --> E[Read when<br/>pointer stable]
    
    style A fill:#fff9c4
    style C fill:#fff9c4

⚠️ Never connect an ammeter in parallel! This creates a short circuit.

Using a Voltmeter

flowchart TD
    A[Select appropriate<br/>voltage range] --> B[Connect in parallel]
    B --> C[Observe polarity<br/>+ to higher potential]
    C --> D[Ensure high<br/>input impedance]
    D --> E[Read when<br/>pointer stable]
    
    style A fill:#fff9c4
    style C fill:#fff9c4

✓ Always connect a voltmeter in parallel! Connecting in series would open the circuit.

Common Mistakes

Mistake Consequence
Ammeter in parallel Short circuit, damage to meter/circuit
Voltmeter in series Circuit opens, no current flows
Wrong polarity Reverse deflection (analog) or negative reading (digital)
Range too low Meter damage or overload
Range too high Poor resolution, hard to read

Multimeter — The Universal Meter

A multimeter combines ammeter, voltmeter, and ohmmeter in one instrument.

Types

Type Characteristics
Analog Pointer on scale; requires interpretation
Digital (DMM) Numeric display; higher accuracy; auto-ranging

Functions

flowchart LR
    A[Multimeter] --> B[DC Voltage]
    A --> C[AC Voltage]
    A --> D[DC Current]
    A --> E[AC Current]
    A --> F[Resistance]
    A --> G[Continuity]
    A --> H[Diode test]

Measurement Accuracy

Factors Affecting Accuracy

  1. Instrument precision — Calibration and quality
  2. Loading effects — Interaction with the circuit
  3. Reading errors — Parallax (analog), resolution (digital)
  4. Environmental factors — Temperature, humidity

Best Practices

  • Choose appropriate instrument for the measurement
  • Account for loading effects in precision work
  • Use null methods (like Wheatstone bridge) for highest accuracy
  • Take multiple readings and average

Worked Examples

Example 1: Ammeter Loading

Given:

  • Circuit with $V = 10$ V and $R = 100$ Ω
  • True current: $I = V/R = 0.1$ A
  • Ammeter with $R_a = 1$ Ω is inserted

Find: Measured current and percent error

Solution:

$$R_{total} = 100 + 1 = 101 \text{ Ω}$$

$$I_{measured} = \frac{10}{101} = 0.099 \text{ A}$$

$$\text{Error} = \frac{0.1 - 0.099}{0.1} \times 100% = 1%$$

Example 2: Voltmeter Loading

Given:

  • Voltage divider: $V_{in} = 12$ V, $R_1 = R_2 = 10$ kΩ
  • True $V_{out} = 6$ V (unloaded)
  • Voltmeter with $R_v = 100$ kΩ is connected

Find: Measured voltage and percent error

Solution:

$$R_{parallel} = \frac{10000 \times 100000}{10000 + 100000} = 9091 \text{ Ω}$$

$$V_{measured} = 12 \times \frac{9091}{10000 + 9091} = 12 \times \frac{9091}{19091} = 5.71 \text{ V}$$

$$\text{Error} = \frac{6 - 5.71}{6} \times 100% = 4.8%$$

Related Concepts

Sources

Key Takeaways

  1. Ammeters measure current and connect in series — low resistance
  2. Voltmeters measure voltage and connect in parallel — high resistance
  3. Loading effects cause measurement errors — choose instruments appropriately
  4. Both are typically constructed from sensitive galvanometers with added resistors
  5. Digital multimeters combine multiple functions with convenience and accuracy