Question

The value of $R$ for which $20\%$ of the main current passes through galvanometer of resistance $80\Omega$ is

• A. $10\Omega$
• B. $20\Omega$
• C. $30\Omega$
• D. $40\Omega$

Answer 1

Answer: (B)

$20\Omega$

Given : 20% of the main current passes through the galvanometer of resistance 80Ω80Ω

Solution :

Let the main current be "i"

Since the Galvanometer and resistance R are connected in parellal so both will have same potential diffrence "v"

Current through Galvanometer is 20% of i

using ohm's law we can write

v=$\frac{20}{100}i\times$80 $\Rightarrow$ v=16i Eq-(1)

Left current will go through resistor R that is 80% of i

using ohm's law in resistor R

v=$\frac{80}{100}i\times$R $\Rightarrow$ v=$\frac{4}{5}iR$ Eq -(2)

From Eq 1 and Eq 2 we get

16i=$\frac{4}{5}$iR

R=20 ohm

The Correct Opt: B