Question

An electric kettle has two coils. When one coil is switched on, it takes 10 min to boil water and when the second coil is switched on it takes 20 min to boil same amount of water. The time taken when both coils are used in parallel is \(n\) seconds. Find \(n\).

Hint:

When devices work together, add their powers (not time). Use \( \frac{1}{t_{\text{total}}} = \frac{1}{t_1} + \frac{1}{t_2} \) for parallel combination.

Answer 1

Correct Answer: 400

Step 1: Understanding the Concept:
For a constant voltage \(V\), heat produced \(H = \frac{V^{2}}{R} t\). Since \(H\) is constant for boiling the same water, \(t \propto R\).
Step 2: Key Formula or Approach:
For parallel resistors: \(\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}\).
By proportionality: \(\frac{1}{t_{p}} = \frac{1}{t_{1}} + \frac{1}{t_{2}}\).
: Detailed Explanation:
Given \(t_{1} = 10\text{ min}\) and \(t_{2} = 20\text{ min}\).
\[ \frac{1}{t_{p}} = \frac{1}{10} + \frac{1}{20} = \frac{2 + 1}{20} = \frac{3}{20} \]
\[ t_{p} = \frac{20}{3}\text{ minutes} \]
Convert minutes to seconds:
\[ n = \frac{20}{3} \times 60 = 20 \times 20 = 400\text{ seconds} \]
Step 3: Final Answer:
The value of \(n\) is \(400\).