Question

A voltmeter has a resistance of $2000\mathrm{ohms}$ and it can measure up to $2\mathrm{V}$. If we want to increase its range to $10\mathrm{V}$, then the required resistance in series will be?

• A. 8000 Omega
• B. 4000 Omega
• C. 6000 Omega
• D. 2000 Omega

Answer 1

The correct option is A

8000 Omega

Step 1: Given information

Resistance of voltmeter, $\mathrm{G}=2000\mathrm{\Omega }$

The initial range of the voltmeter is ${\mathrm{V}}_{\mathrm{given}}=2\mathrm{V}$

A new range of voltmeters is ${\mathrm{R}}_{\mathrm{given}}=10\mathrm{V}$

Step 2: Calculating Resistance

We know the formula,

$\mathrm{R}=(\mathrm{n}-1)\mathrm{G}$

Here,

n_V is the range of voltmeter.

R is the required resistance.

G is the voltmeter resistance.

Now,

$$\begin{gathered} \mathrm{n}=\frac{{\mathrm{R}}_{\mathrm{given}}}{{\mathrm{V}}_{\mathrm{given}}} \\ =\frac{10}{2} \\ =5 \end{gathered}$$

By substituting the values in the above formula, we get

$$\begin{gathered} \mathrm{R}=(5-1)\times 2000 \\ =4\times 2000 \\ =8000\mathrm{\Omega } \end{gathered}$$

Therefore, the required resistance in series will be $8000\mathrm{\Omega }$.

Hence, option (A) is the correct answer.