Question

An electric kettle has two coils when one of these is switched on. the water in the kettle boils in 6 minutes. When the other coil is switched on, boils in 3 minutes If the two coils are connected in parallel, the time taken to boil water in the kettle is. (A) 3 minutes (B) 6 minutes (C) 2 minutes (D) 9 minutes

Short answer

The time taken to boil water when both coils are connected in parallel is 2 minutes. The correct answer is (C) 2 minutes.

Step-by-step solution

1. Calculate the Power Associated with Each Coil Individually

First, let's calculate the power of each coil when it heats up the water on its own. We can use the formula: Power = Work / Time Since we don't know the specific work done by each coil, we can use a constant C to represent the work done in boiling the water. We know that: Power_1 = C / 6 (for the first coil that takes 6 minutes) Power_2 = C / 3 (for the second coil that takes 3 minutes)

2. Determine the Equivalent Power for Parallel Connection

Next, we need to find the equivalent power of the two coils connected in parallel. In a parallel connection, the total power is the sum of the individual powers of the coils. So, we can write: Power_total = Power_1 + Power_2

3. Calculate the Total Power and Express in Terms of C

Plug in the values of Power_1 and Power_2 from step 1 in the equation above, we get: Power_total = (C / 6) + (C / 3) By solving for Power_total, we get: Power_total = C / 2

4. Determine the Time Taken to Boil Water with the Equivalent Power

Now we need to find the time taken to boil water with the equivalent power when both coils are connected in parallel. We can use the same formula as in step 1. Therefore, Time_total = Work / Power_total Plugging in the total power and the work done constant C, we get: Time_total = C / (C / 2)

5. Calculate the Time_total for Coils Connected in Parallel

By solving the equation in step 4, we get: Time_total = 2 So, when both coils are connected in parallel, the time taken to boil water is 2 minutes. The correct answer is (C) 2 minutes.

Key concepts

Electric Power

Electric power is the rate at which electrical energy is used by appliances, such as an electric kettle. This concept is crucial for understanding how quickly appliances like kettles can heat water. Power is calculated using the formula:

• Power = Work / Time

This formula indicates that power is the amount of work done per unit of time. Work, in this context, refers to the energy required to heat water to its boiling point.
When an electric kettle is in use, the coils inside the kettle convert electrical energy into heat energy, which then heats the water. The power output of a coil depends on its efficiency and the time taken to complete the task.
If you know how much time a specific coil takes to boil water, you can calculate the power of that coil. For example, if it takes one coil 6 minutes and another 3 minutes, you can find their respective power outputs by replacing 'Time' with those minutes in the formula. The shorter the time, the higher the power output, since the same amount of work is done in less time.

Parallel Circuits

Parallel circuits are a way of connecting electrical components such that the current can take multiple paths. In an electric kettle with coils in parallel, each coil has its own separate path for the electric current. This configuration is why the total power used by the kettle is the sum of the power used by each coil.
Parallel circuits offer some distinct advantages:

• Each component gets the same voltage.
• If one component fails, others can still function.

For the kettle, connecting coils in parallel means you can combine their efforts, resulting in more power and, consequently, quicker boiling. The power from each coil adds up, leading to a higher overall power output. When they work together, they can complete the task faster than when working individually. This is why the boiling time decreases when both coils operate in parallel.

Boiling Time Calculation

To calculate the boiling time when coils are connected in parallel, you need to find the combined power output first. In our exercise, coil 1 and coil 2 have individual powers defined as:

• Power_1 = C / 6
• Power_2 = C / 3

Here, C represents the constant work needed to boil the water. When combined in parallel, the total power (Power_total) is their sum:

• Power_total = Power_1 + Power_2 = (C / 6) + (C / 3)

This simplifies to:

• Power_total = C / 2

Finally, use the power formula again to find the time it will take to boil the water with this new total power:

• Time_total = Work / Power_total

Here, Time_total equals 2 minutes, showing that with both coils connected in parallel, boiling is much faster compared to using either coil alone. This calculation demonstrates how parallel configurations can enhance the efficiency of electric appliances.