In the circuit (Figure) the current is to be measured. What is the value of the current if the ammeter shown:
$(a)$ is a galvanometer with a resistance $R_{G}=60.00 \; \Omega$;
$(b)$ is a galvanometer described in $(a)$ but converted to an ammeter by a shunt resistance $r_{s}=0.02 \; \Omega$;
$(c)$ is an ideal ammeter with zero resistance?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Total resistance in the circuit is $R_{total} = R_{G} + 3.00 \; \Omega = 60.00 \; \Omega + 3.00 \; \Omega = 63.00 \; \Omega$.
Using Ohm's law,the current $I = V / R_{total} = 3.00 \; \text{V} / 63.00 \; \Omega \approx 0.0476 \; \text{A} \approx 0.048 \; \text{A}$.
$(b)$ The resistance of the galvanometer converted to an ammeter is $R_{A} = \frac{R_{G} \cdot r_{s}}{R_{G} + r_{s}} = \frac{60.00 \; \Omega \times 0.02 \; \Omega}{60.00 \; \Omega + 0.02 \; \Omega} = \frac{1.2}{60.02} \; \Omega \approx 0.01999 \; \Omega \approx 0.02 \; \Omega$.
Total resistance in the circuit is $R_{total} = R_{A} + 3.00 \; \Omega = 0.02 \; \Omega + 3.00 \; \Omega = 3.02 \; \Omega$.
Using Ohm's law,the current $I = V / R_{total} = 3.00 \; \text{V} / 3.02 \; \Omega \approx 0.993 \; \text{A} \approx 0.99 \; \text{A}$.
$(c)$ For an ideal ammeter,the resistance is zero. Thus,the total resistance is $3.00 \; \Omega$.
The current $I = V / R = 3.00 \; \text{V} / 3.00 \; \Omega = 1.00 \; \text{A}$.

Explore More

Similar Questions

Mark out the correct options.

$A$ moving coil galvanometer has a resistance of $50\,\Omega$ and it indicates full-scale deflection at a current of $4\,mA$. $A$ voltmeter is constructed using this galvanometer and a $5\,k\Omega$ series resistance. The maximum voltage that can be measured using this voltmeter will be close to ......$V$.

Current sensitivities of two galvanometers $G_1$ and $G_2$ of resistances $100 \ \Omega$ and $50 \ \Omega$ are $10^8 \ \text{div/A}$ and $0.5 \times 10^5 \ \text{div/A}$ respectively. The galvanometer in which the voltage sensitivity is more is

Shunt wire should be . . . . . . .

When a shunt of $4\,\Omega$ is attached to a galvanometer,the deflection reduces to $\frac{1}{5}$th of its initial value. If an additional shunt of $4\,\Omega$ is attached in parallel to the first,what will be the new deflection?

Difficult
View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo