Question

Two equal resistors are first connected in series and then in parallel in a circuit across same potential difference. The ratio of their power in series and parallel combination will be:

• A. 1:2
• B. 2:1
• C. 1:4
• D. 4:1

Answer 1

The correct option is C 1:4

The equivalent resistance in series connection would be ‘2R’ and hence the current flowing would be $\frac{V}{2R}$.
Now, Power developed across any resistor is simply the product of the potential difference across the resistor and the current flowing through it. So, Power developed in series connection $=\frac{(V\times V)}{2R}=\left(\frac{V^2}{2R}\right).$
In parallel connection the equivalent resistance shall be come $\frac{R}{2}$ and so the current through it would be $\frac{2V}{R}$.
Likewise, power developed $=\frac{(V\times 2V)}{R}=\frac{2V^2}{R}.$
So, ratio of power developed in series to that in parallel would be $\left(\frac{\frac{V^2}{2R}}{\frac{2V^2}{R}}\right)=1:4$