Question

Four identical resistors are wired as shown in the diagram below.
If the resistance of each is $R$, what is the equivalent resistance of this combination?

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

Answer 1

Answer: (D)

$R$

Equivalent resistance of resistances connected in parallel in loop 1 $\frac{1}{r_1}=\frac{1}{R}+\frac{1}{R}$

$⟹$ $r_1=\frac{R}{2}$

Similarly $r_2=\frac{R}{2}$

Now equivalent resistance of the circuit $R_{eq}=r_1+r_2=\frac{R}{2}+\frac{R}{2}=R$