Physics Q37 – JEE-MAIN 2026

Home Physics Current ElectricityQuestion #38

A voltmeter with internal resistance of

r Ω

can be used to measure upto

20 V

. In order to increase its measuring range to

30 V

, the required modification is to _______.

Clue 1 of 3: Voltmeter Range Extension

To increase the measuring range of a voltmeter, an additional resistance must be connected in series with its internal resistance.

🧠 Full Solution Path

Step 1: Determine Full-Scale Deflection Current✦ Active

The initial range of the voltmeter is $V_{1} = 20 V$ with internal resistance $R_{v} = r$ . The full-scale deflection current $I_{g}$ is given by $V_{1} = I_{g} R_{v}$ .

I_{g} = \frac{V_{1}}{R_{v}} = \frac{20}{r}

Step 2: Calculate Required Total Resistance for New Range○ Expand

To increase the range to $V_{2} = 30 V$ , an additional series resistance $R_{s}$ must be connected. The total resistance of the voltmeter circuit will be $R_{t o t a l}^{'} = R_{v} + R_{s} = r + R_{s}$ . The new range is given by $V_{2} = I_{g} (R_{v} + R_{s})$ .

30 = (\frac{20}{r}) (r + R_{s})

Step 3: Solve for the Additional Series Resistance○ Expand

From the equation in Step 2, we can solve for $R_{s}$ :

30 r = 20 (r + R_{s})

30 r = 20 r + 20 R_{s}

10 r = 20 R_{s}

R_{s} = \frac{10 r}{20} = \frac{r}{2}

Thus, a resistor of $\frac{r}{2} Ω$ must be connected in series with the voltmeter.

💡 Teacher's Secret Hint

Remember that a voltmeter's range is extended by adding resistance in series, not parallel.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Physics Question 37 – JEE-MAIN 2026

Clue 1 of 3: Voltmeter Range Extension

🧠 Full Solution Path