Question

A galvanometer of resistance $10ohm$ and maximum current of$2\mu A$ is converted into voltmeter of range $100mV$ and when converted into ammeter then range is $1mA$. When these voltmeter and ammeter are connected by a (ideal) battery in series with a resistance of$R=1000\Omega$, then

• A. Measured value of $R$ is between$978\Omega and996\Omega$
• B. If the ideal battery is replaced by non-ideal battery with internal resistance of $5\Omega$ then $R$ will be $>1000\Omega$
• C. Shunt resistance is $20m\Omega$
• D. Resistance of voltmeter ${10}^5\Omega$

Answer 1

Answer: (A), (C)

Shunt resistance is $20m\Omega$

Step 1. Given data:

Maximum current flowing through Galvanometer, $I_g=2\mu A$,

$I_g=2\times {10}^{-6}A$

Range of the voltmeter, $V=100mV$,

$V=100\times {10}^{-3}V$

Range of Ammeter, $I=1mA$,

$I=1\times {10}^{-3}A$

Resistance of Galvanometer, $R_g=10\Omega$ ,

Additional resistance connected, $R=1000\Omega$,

$R_v=$ Resistance of Voltmeter

$R_A=$ Resistance of Ammeter

Explanation for the correct options

Step 2. Check Option $\left(C\right)$, if it is correct:

As an ammeter,

Resistance of ammeter $R_A=\frac{G\times Rs}{G+Rs}$
$i=i_g\left(\frac{R_s+G}{R_s}\right)$

$i=i_g\left(\frac{r_g}{R_s}\right)$
from the given data,
$1mA=2\times {10}^{-6}\left(\frac{10}{R_s}\right)$

$R_s=0.02\Omega$

$R_s=20m\Omega$
Hence option $\left(B\right)$ is correct.

Step 3. Check Option $\left(A\right)$, if it is correct:

For option A,

Req$=980.48\Omega$

$I=\frac{V_0}{980.48}$ and $V\prime =\frac{V_0\times 50000}{980.48\times 51}$

$R_{\left(measured\right)}=\frac{V\prime }{I}=\frac{50000}{51}=980.4\Omega$

Where the measured value of $R$ is between$978\Omega and996\Omega$

Hence option $\left(A\right)$ is correct.

Explanation for the incorrect options:

Step 4. Check Option $\left(D\right)$, if it is correct:
As a voltmeter $V=i_g(r_g+R_0)$(where, $R_0=$ shunt resistance)

reading of voltmeter $=100\times {10}^{-3}$
so, $100\times {10}^{-3}=2\times {10}^{-6}(10+R_0)$

$R_0=50k\Omega$
Hence option $\left(D\right)$ is wrong.

Step 5. Check Option $\left(B\right)$, if it is correct:

Thus, The maximum value of resistance can not be greater than $1000\Omega$. Internal resistance of cell will not affect the total resistance measurement.

Hence, option $\left(B\right)$ is incorrect.

Hence, the correct option are $\left(A\right),\left(C\right)$.