The sliding contact C is at one fourth of the length of the...

The sliding contact

C

is at one fourth of the length of the potential wire

(A B)

from

A

as shown in the circuit diagram. If the resistance of the wire

A B

R_0

, then the potential drop

(V)

across the resistor

R

is:

The sliding contact C is at one fourth of the length of the potential wire (A B) from A as shown in the circuit

Options

A $\frac{4 \mathrm{~V}_0 R}{3 \mathrm{R}_0+16 R}$
B $\frac{4 V_0 R}{3 R_0+R}$
C $\frac{2 V_0 R}{4 R_0+R}$
D $\frac{2 V_0 R}{2 R_0+3 R}$

Correct answer

A. $\frac{4 \mathrm{~V}_0 R}{3 \mathrm{R}_0+16 R}$

Step-by-step solution

The given diagram can be redrawn as follow: The sliding contact C is at one fourth of the length of the potential wire (A B) from A as shown in the circuit

The potential across

A C

\mathrm{V}_{\mathrm{AC}}=\frac{\mathrm{R}_{\mathrm{AC}}}{\mathrm{R}_{\mathrm{BC}}+\mathrm{R}_{\mathrm{AC}}} \times \mathrm{V}_0

\begin{aligned} & \frac{\frac{R R_0}{4 R+R_0}}{\frac{3 R_0}{4}+\frac{R R_0}{4 R+R_0}} \times V_0 \\ & = \frac{4 R V_0}{3 R_0+16 R} \end{aligned}

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