Question

If resistance of a conductor is kept constant and voltage through the appliance is reduced to half. Then, the resultant power is___.

• A. $\frac{1}{2}$ $\times$ P
• B. $\frac{1}{4}$ $\times$ P
• C. 4 $\times$ P
• D. $\frac{1}{8}$ $\times$ P

Answer 1

The correct option is B $\frac{1}{4}$ $\times$ P

Given, power = P (constant)
resistance of conductor = R (constant)
voltage = V

According to formula of power we have,
P = $\frac{V²}{R}$
If new voltage is V' = $\frac{V}{2}$
we get, resultant power as,
P' = $\frac{V²}{4R}$
P' = $\frac{1}{4}$ $\times$ $\frac{V²}{R}$
Or
P' = $\frac{1}{4}$ $\times$ P

Therefore, if we half the voltage through the conductor with the resistance constant, the power across the conductor is reduced to a quarter of the original value.