Question

When two unknown resistances are placed in the gaps of meterbridge, the null point is found to be $40cm$ from one end of the bridge wire. When one of the resistances is shunted with a $10$ ohm coil, the null point is $25cm$ from the same end. The value of each of the unknown resistances is

• A. $15\Omega ,10\Omega$
• B. $10\Omega ,15\Omega$
• C. $20\Omega ,30\Omega$
• D. $30\Omega ,20\Omega$

Answer 1

Answer: (B)

$10\Omega ,15\Omega$

Let the Resistance of P be $R_1$ and Q be $R_2$

$\frac{R_1}{R_2}=\frac{l}{100-l}=\frac{40}{60}=2/3$

As after shunting l value decreased the shunting is done on $R_1$

After shunting $R_{eff}=\frac{10R_1}{10+R_1}$

$\Rightarrow \frac{R_{eff}}{R_2}=\frac{25}{75}=1/3$

$R_{eff}=\frac{R_2}{3}$

$R_{eff}=R_{1/2}$

$\Rightarrow \frac{10}{10+R_1}=/2$

$20=10+R_1$

$\frac{10}{R_2}=2/3\Rightarrow R_2=15$

$\Rightarrow R_1=10\Omega$