Two heating coils of resistances \( 10 \Omega \) and \( 20 \Omega \) are connected in parallel and connected to a
battery of emf \( 12 \mathrm{~V} \) and internal resistance \( 1 \Omega \). The power consumed by them are in the ratio

• A

  $1: 4$
• B

  \( 1: 3 \)
• Correct answer
  C

  \( 1 \)
• D

  \( 04: 1 \)

Solution

Since the resistors are connected in parallel, then potential difference across each resistor is same. Power is given as
\[ \begin{array}{l} P=\frac{V^{2}}{R} \\ \Rightarrow P \propto \frac{1}{R} \\ \Rightarrow \frac{P_{1}}{P_{2}}=\frac{R_{2}}{R_{1}} \\ \Rightarrow \frac{P_{1}}{P_{2}}=\frac{20}{10}=\frac{2}{1} \end{array} \]
Therefore, the power consumed by them are in the ratio \( 2: 1 \).

Hence, the correct answer is option: 'C'.