Question

A circuit is created with a source and four identical resistors of resistance $R$ as shown above.
The equivalent resistance of the circuit is:

• A. $\frac{1}{2}R$
• B. $\frac{2}{3}R$
• C. $R$
• D. $\frac{5}{3}R$
• E. $4R$

Answer 1

Answer: (D)

$\frac{5}{3}R$

We can see from the given circuit , that $R_3$ and $R_4$ are in series , therefore equivalent resistance

$R^{\prime }=R+R=2R$

now , $R^{\prime }$ and $R_2$ are in parallel , therefore equivalent resistance

$R^{\prime \prime }=\frac{R\times 2R}{R+2R}=2R/3$

since $R_1$ and $R^{\prime \prime }$ are in series , therefore final equivalent resistance

$R^{\prime \prime \prime }=2R/3+R=5R/3$