Ammeter and Voltmeter — Revision Notes

⚡ 30-Second Revision

Galvanometer: — $R_g$ (resistance), $I_g$ (full-scale current).
Ammeter Conversion: — Shunt resistance $R_s$ in parallel with $R_g$.

- Formula: $R_s = \frac{I_g R_g}{I - I_g}$ - Ideal Ammeter: $R_{eff} = 0$, connected in series.

Voltmeter Conversion: — Series resistance $R_{ser}$ in series with $R_g$.

- Formula: $R_{ser} = \frac{V}{I_g} - R_g$ - Ideal Voltmeter: $R_{eff} = \infty$, connected in parallel.

Key Principle: — Ammeters in series, Voltmeters in parallel.

2-Minute Revision

Ammeters and voltmeters are crucial measuring instruments derived from a galvanometer. A galvanometer is a sensitive device with internal resistance $R_g$ and a maximum current $I_g$ for full-scale deflection.

To convert it into an ammeter, a small resistance called a shunt ($R_s$) is connected in parallel with the galvanometer. This allows most of the current ($I - I_g$) to bypass the galvanometer, extending its range.

The formula is $R_s = \frac{I_g R_g}{I - I_g}$. Ammeters must be connected in series and ideally have zero internal resistance to avoid affecting the circuit current.

To convert a galvanometer into a voltmeter, a large resistance ($R_{ser}$) is connected in series with the galvanometer. This resistance drops most of the voltage, allowing the galvanometer to measure higher potential differences.

The formula is $R_{ser} = \frac{V}{I_g} - R_g$. Voltmeters must be connected in parallel and ideally have infinite internal resistance to avoid drawing current from the circuit. Remember, incorrect connections (ammeter in parallel, voltmeter in series) can damage the instruments or severely disrupt the circuit.

5-Minute Revision

Let's consolidate the core concepts of ammeters and voltmeters for NEET. Both instruments originate from a galvanometer, which is a current-sensitive device characterized by its internal resistance ($R_g$) and the current required for full-scale deflection ($I_g$).

Ammeter: Used to measure current. To convert a galvanometer into an ammeter, a very small resistance, known as a **shunt resistance ($R_s$)**, is connected in *parallel* with the galvanometer. This parallel connection ensures that the majority of the total current ($I$) bypasses the sensitive galvanometer coil, with only $I_g$ flowing through it.

The potential difference across the parallel combination is equal: $I_g R_g = (I - I_g) R_s$. From this, $R_s = \frac{I_g R_g}{I - I_g}$. An ammeter must always be connected in *series* with the component whose current is to be measured.

Ideally, an ammeter has zero internal resistance to prevent it from altering the circuit's current. Its effective resistance is $R_{eff,A} = \frac{R_g R_s}{R_g + R_s}$, which is very small.

Voltmeter: Used to measure potential difference. To convert a galvanometer into a voltmeter, a very large resistance, called a **series resistance ($R_{ser}$)**, is connected in *series* with the galvanometer.

This series resistance drops most of the voltage ($V$), allowing only $I_g$ to flow through the galvanometer for full-scale deflection. The total voltage across the combination is $V = I_g (R_g + R_{ser})$.

From this, $R_{ser} = \frac{V}{I_g} - R_g$. A voltmeter must always be connected in *parallel* across the points where the voltage is to be measured. Ideally, a voltmeter has infinite internal resistance to prevent it from drawing any current from the circuit, thus not altering the potential difference.

Its effective resistance is $R_{eff,V} = R_g + R_{ser}$, which is very large.

Key Takeaways:

Ammeter: — Shunt (parallel, small $R$), Series connection, Ideal $R=0$.
Voltmeter: — Series resistor (series, large $R$), Parallel connection, Ideal $R=\infty$.
Common Errors: — Connecting ammeter in parallel (short circuit), voltmeter in series (open circuit). Be mindful of practical meter internal resistances and their 'loading effect' on measurements.

Prelims Revision Notes

Ammeter and Voltmeter: NEET Revision Notes

1. Galvanometer (G):

A current-detecting device. Has internal resistance $R_g$ and full-scale deflection current $I_g$.
Principle: Torque on current loop in magnetic field.

2. Ammeter:

Purpose: — Measures current.
Conversion: — Galvanometer converted by connecting a **shunt resistance ($R_s$) in parallel** with it.
Reason for Shunt: — To bypass most of the current, allowing only $I_g$ through the galvanometer, and to reduce the overall resistance of the instrument.
Formula for Shunt Resistance: — $R_s = \frac{I_g R_g}{I - I_g}$, where $I$ is the desired range of the ammeter.
Connection in Circuit: — Always in series with the component whose current is to be measured.
Ideal Ammeter: — Has zero internal resistance. (Practical ammeters have very low resistance).
Effective Resistance of Ammeter: — $R_{eff,A} = \frac{R_g R_s}{R_g + R_s}$. This is always less than $R_g$.
Range Extension: — To increase the range ($I$), decrease $R_s$.

3. Voltmeter:

Purpose: — Measures potential difference (voltage).
Conversion: — Galvanometer converted by connecting a **series resistance ($R_{ser}$) in series** with it.
Reason for Series Resistor: — To drop most of the voltage across itself, limiting the current through the galvanometer to $I_g$, and to increase the overall resistance of the instrument.
Formula for Series Resistance: — $R_{ser} = \frac{V}{I_g} - R_g$, where $V$ is the desired range of the voltmeter.
Connection in Circuit: — Always in parallel across the points between which voltage is to be measured.
Ideal Voltmeter: — Has infinite internal resistance. (Practical voltmeters have very high resistance).
Effective Resistance of Voltmeter: — $R_{eff,V} = R_g + R_{ser}$. This is always greater than $R_g$.
Range Extension: — To increase the range ($V$), increase $R_{ser}$.

4. Common Mistakes/Important Points:

Ammeter in Parallel: — Short circuits the component, damages ammeter/source.
Voltmeter in Series: — Acts as an open circuit, stops current flow.
Unit Conversion: — Always convert mA to A ($1,\text{mA} = 10^{-3},\text{A}$) for calculations.
Loading Effect: — Practical meters alter the circuit slightly due to their non-ideal internal resistances. Ammeters slightly reduce current, voltmeters slightly reduce voltage.

Vyyuha Quick Recall

Ammeter: All in Series, Shunt in Parallel, Small resistance. (Ammeter, All in Series connection, Shunt is in Parallel, Shunt is Small resistance)

Voltmeter: Very Parallel, Series resistor, Large resistance. (Voltmeter, Very Parallel connection, Series resistor, Series resistor is Large resistance)