Question

please answer finding reading of voltmeter​

Answer 1

Question:- Two resistances of 100 ohms and 200 ohm are connected in series to a 150 V supply.A voltmeter of resistance of 200 ohm is connected across 100 ohm resistor.what will be the reading of voltmeter

Soln:-

Given

• Two resistances of 100 ohm and 200 ohm are connected in series.

• A voltmeter having internal resistance of 200 ohm is connected across 100 ohm resistor.

See the image attached for diagram.

To Find

Reading of Voltmeter

Concept

• Voltmeter measures potential difference across the two point it is connected.Hence, here, it will the measure the potential difference across 100 ohm resistor.

• In series combination of resistance , equivalent resistance is measured by the relation

$R_{eq} = R_1 + R_2 + R_3 + R_4....$

• In parallel combination , we measure equivalent resistance as

$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ......$

Solutions

$\green{Finding\:net\:resistance\:across\:100\:ohm\:resistor}$

• Voltmeter (200 ohm) and 100 ohm resistor are parallel.

$\frac{1}{R_{eq}} = \frac{1}{200} + \frac{1}{100} +$

=> $\frac{1}{R_{eq}} = \frac{3}{200}$

=> $\frac{1}{R_{eq}} = \frac{3}{200}$

=> $R_{eq}= \frac{200}{3}$

$\green{Finding\:net\:resistance\:in\:the\:circuit}$

• Net resistance will be the sum of $R_{eq}$ and 200 ohm

= $R_{eq} + 200$

= $\frac{200}{3}\:+\: 200$

= $\frac{800}{3}$

$\green{Finding\:net\:current\:in\:the\:circuit}$

=> I = $\frac{V}{R}$

=> I = $\frac{150\:×\:3}{800}$ A

=> I = $\frac{9}{16}$ A

$\green{Finding\:net\:reading \:of\:the\:voltmeter}$

• Reading of the Voltmeter = Current flowing × Net resistance across it

= $\frac{200}{3} × \: \frac{9}{16}$

= $\frac{75}{2}$

= 37.5 V

$\boxed{\boxed{\pink{The\:reading\:of\:the\:voltmeter\:is\:37.5\:V}}}$