Question

Two identical heater wires are first connected in series and then in parallel with a source of electricity. The ratio of heat produced in the two cases ?

• A. $2:1$
• B. $1:2$
• C. $4:1$
• D. $1:4$

Answer 1

The correct option is D $1:4$

Answer is D.

The heat energy E = Pt = (VI)t = $I^{2}Rt(V=IR)$.
Since the wires are identical, their resistances are equal. Let their individual resistance be R.
In series, the equivalent resistance is R+R = 2R.
Therefore, E1 = $I^2\left(2R\right)t=2\left(I^{2}Rt\right)$.
In parallel, the equivalent resistance = $\frac{R^2}{2R}$.
Therefore, E2 = $I^2\left(\frac{R^2}{2R}\right)t=\frac{I^{2}Rt}{2}$.
E1/E2 = 1/4.
Hence, the ratio is 1:4.