Question

When a current of $5mA$ is passed through a galvanometer having a coil of resistance of $15\Omega$, it shows full-scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of the range $0-10V$ is:

• A. $1.985\times {10}^3\Omega$
• B. $2.045\times {10}^3\Omega$
• C. $2.535\times {10}^3\Omega$
• D. $4.005\times {10}^3\Omega$

Answer 1

The correct option is A

$1.985\times {10}^3\Omega$

Step 1: Given data-

Current passing through galvanometer ($I_g$) $=5mA=5\times {10}^{-3}A$

Resistance of galvanometer $\left(G\right)$$=15\Omega$

Voltage taken $\left(V\right)$$=10V$

Step 2: Formula used-

$V=I_g(R+G)$

assume $R$ be the series resistance.

Step 3: Calculating series resistance.

Putting all the given values in the formula,

$$\begin{gathered} V=I_g(R+G) \\ 10=5\times {10}^{-3}(R+15) \\ R=2000–15=1985=1.985\times {10}^3\Omega \end{gathered}$$

Thus, Option A is the correct answer that is the resistance to be put in series with the galvanometer is $1.985\times {10}^3\Omega$.