Question

A heater coil connected across a given potential difference has power P. Now, the coil is cut into two equal halves and joined in parallel. Across the same potential difference, this combination has power.
A. P
B. 4P
C. $\dfrac{p}{4}$​
D. 2P

Answer 1

Hint: As per the above question, the two coils are connected parallel to each other with a potential difference. Hence we need to use the formula of parallel combination of resistance. Then we can find out the power of a coil.

Complete step by step answer:
From a given data heater coil connected across a potential difference has power .The coil is cut into two equal halves and joined parallel.Let us assume the coil has resistance R and the coil is cut into two equal halves. Therefore each coil produces resistance $\dfrac{R}{2}$ each.
If both the coils connected in parallel then by using the formula,
$
\dfrac{1}{{{R_p}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} \\
\Rightarrow\dfrac{1}{{{R^1}}} = \dfrac{2}{R} + \dfrac{2}{R} \\
\Rightarrow\dfrac{1}{{{R^1}}} = 2\left( {\dfrac{2}{R}} \right) \\
\Rightarrow\dfrac{1}{{{R^1}}} = \dfrac{4}{R} \\
\therefore{R^1} = \dfrac{R}{4} \\ $
Where, ${R^1}$=total resistance
So the resistance has decreased by a factor 4.
$P = \dfrac{{{V^2}}}{R}$
Power is inversely proportional to R when V is constant.

If R decreases by a quantity 4, then P is increased by a quantity 4.Hence,the correct option is B.

Note:Students might have confusion in the parallel and series combination circuits. In parallel, the resistance is connected at the same point of both ends. In series combination the resistance is connected one end to another end of the resistor.