Question

In a network as shown in the figure, the potential difference across the resistance $2R$ is (the cell has an emf of $E$ volts and has no internal resistance)

• A. $2E$
• B. $\frac{4E}{7}$
• C. $\frac{E}{7}$
• D. $E$

Answer 1

Answer: (B)

Potential difference across resistors connected in parallel is same.
In the given circuit, resistors $4R$ and $2R$ are connected in parallel while resistance $R$ is connected in series to it. Hence, equivalent resistance is

$\frac{1}{R^{{}^{\prime }}}=\frac{1}{4R}+\frac{1}{2R}=\frac{6R}{8R^2}$
$R^{{}^{\prime }}=\frac{8}{6}R=\frac{4}{3}R$
$\Rightarrow R^{{}^{\prime \prime }}=R+\frac{4}{3}R=\frac{7R}{3}$
Given, emf is $E$ volts, therefore

$i=\frac{E}{R}=\frac{3E}{7R}$
Potential difference across $R$ is
$V=ir=\frac{3E}{7R}\times R=\frac{3E}{7}$
Potential difference across $2R$ is
$V^{{}^{\prime }}=E-\frac{3E}{7}=\frac{4E}{7}$
Note : Potential drop across $4R$ resistor is same as that across $2R$, since both are connected in parallel.