Question 230: Current Electricity

Question

A galvanometer has a resistance of $50 ~\Omega$ and it allows maximum current of $5 \mathrm{~mA}$. It can be converted into voltmeter to measure upto $100 \mathrm{~V}$ by connecting in series a resistor of resistance :

Accepted Answer

To convert a galvanometer into a voltmeter to measure higher voltages, you need to add a series resistance to it. Let's figure out the required resistance value.
First, let's find the maximum voltage that can be directly measured by the galvanometer without any additional resistance. We know the maximum current, $I$, that the galvanometer can safely measure is $5 	ext{ mA}$, and the resistance of the galvanometer, $R_g$, is $50 \Omega$.
Using Ohm's law $ V = I 	imes R $, the maximum voltage $V_g$ the galvanometer can measure is:
$ V_g = I 	imes R_g $
$ V_g = 5 	imes 10^{-3} 	ext{ A} 	imes 50 \Omega $
$ V_g = 0.25 	ext{ V} $
Next, to measure up to $100 	ext{ V}$, we need to add a series resistor $R_s$ so that the total voltage drop when the maximum current is flowing is $100 	ext{ V}$. The voltage drop across the additional resistor $R_s$ when the maximum current flows would be the total voltage minus the voltage across the galvanometer:
$ V_s = V_{	ext{total}} - V_g $
$ V_s = 100 	ext{ V} - 0.25 	ext{ V} $
$ V_s = 99.75 	ext{ V} $
Applying Ohm's law to the series resistor to find its resistance value:
$ R_s = \frac{V_s}{I} $
$ R_s = \frac{99.75 	ext{ V}}{5 	imes 10^{-3} 	ext{ A}} $
$ R_s = 19950 \Omega $
Therefore, the resistance of the series resistor required to convert the galvanometer into a voltmeter that can measure up to $100 	ext{ V}$ is $19950 \Omega$.
The correct option is D: $19950 \Omega$.

Answer

$19500 \Omega$

Answer

$5975 \Omega$

Answer

$20050 \Omega$

Answer

$19950 \Omega$

Current Electricity

A galvanometer has a resistance of 50 ~\Omega and it allows maximum current of 5 \mathrm{~mA}. It can be converted into voltmeter to measure upto 100 \mathrm{~V} by connecting in series a resistor of resistance :

Choose the correct answer: