Question

Find the equivalent resistance about any branch of the base of the square pyramid shown. Assume resistance of each branch is R

• A. $\frac{7R}{15}$
• B. $\frac{8R}{15}$
• C. $\frac{R}{2}$
• D. None of these

Answer 1

Answer: (B)

$\frac{8R}{15}$

The given circuit is converted to its equivalent circuit, as shown in figure.

The equivalent resistance in branches AD, AB and BC is

$R_s=R+\frac{2R}{3}+R$

$R_s=2R+\frac{2R}{3}$

$R_s=2R+\frac{2R}{3}$

$R_s=\frac{8R}{3}\Omega$

The equivalent resistance in branch CD is

$\frac{1}{R_{eq}}=\frac{3}{8R}+\frac{3}{2R}$

$\frac{1}{R_{eq}}=\frac{15}{8R}$

$R_{eq}=\frac{8R}{15}\Omega$