Question

A voltmeter of 900 ohm connected in series with resistance R in a circuit reads 198 V. When R is replaced by 2R,the voltmeter reads 180 volts. what is the value of R

Answer 1

Answer: 100 Ω

Explanation:

The resistance of the voltmeter, Rv = 900 Ω

Let the applied voltage across the loop be denoted as “V”.

Step 1:

Here, when the voltmeter is connected in series with the resistance R, then it indicates a voltage of 198 V.

The current flowing across the potentiometer will be,

i = Voltage/Resistance = (198/900) A

So, the potential drop across the resistance R, Vr = i * R = (198/900)*R

Applying KVL across the loop, we have

Vr + 198 = V

⇒ i*R + 198 = V  

⇒ V = (198/900)*R + 198 ….. (i)

Step 2:

It is given that, when the resistance R is replaced by 2R, the voltmeter indicates a voltage of 180 V.

Here, the current flowing across this potentiometer will be,

i = (180/900) A

So, the potential drop across the resistance 2R, Vr = i * 2R = (180/900)*2R

Applying KVL across the loop, we have

Vr + 180 = V

⇒ i*2R + 180 = V  

⇒ V = (180/900)*2R + 180 ….. (ii)

Step 3:

Equating eq. (i) & (ii), we get

(198/900)*R + 198 = (180/900)*2R + 180

⇒ 198 – 180 = (360/900)*R - (198/900)*R

⇒ 18 = [(360 – 198)/900]*R

⇒ 18 = [162/900]*R

⇒ R = [900 * 18] / 162 = 100 Ω

Thus, the value of R is 100 Ω.