Question

A uniform wire of resistance $50\Omega$ is cut into 4 equal parts which are then connected in parallel. What is the effective resistance of the combination?

• A. $3.125\Omega$
• B. $5.125\Omega$
• C. $1.750\Omega$
• D. $2.025\Omega$

Answer 1

The correct option is A $3.125\Omega$

We know that resistance, R $\propto$ length of wire.
Since the wire of resistance $50\Omega$ is cut into four equal parts, the resistance of each piece will be $\frac{50}{4}$ = $12.5\Omega$.
When these new four resistances are connected in parallel, the effective resistance ($R_{eff}$) of the combination is given by:
$\frac{1}{R_{eff}}=\frac{1}{12.5}+\frac{1}{12.5}+\frac{1}{12.5}+\frac{1}{12.5}=\frac{4}{12.5}$
$⟹$ $R_{eff}=\frac{12.5}{4}=3.125\Omega$.