Question

A coffee machine transfers 12 kJ of energy in 15 seconds. It uses the 230 V mains supply. Use this information to work out the current through the coffee machine. Give your answer to two significant figures.

Answer 1

To find the current through the coffee machine, convert the energy to joules, calculate power using the energy and time, and then use the power formula with the given voltage. The current is found to be approximately 3.48 amperes.

Step-by-step explanation:

To solve the mathematical problem completely, we need to determine the current through the coffee machine using the given data: energy transferred (12 kJ) and time (15 seconds), and that it uses a 230 V mains supply.

First, convert energy from kilojoules to joules since power is typically measured in watts (joules per second):
1 kJ = 1000 J
So, 12 kJ = 12,000 J.

Now, calculate the power (P) using the formula P = Energy / Time. Here, energy is 12,000 J and time is 15 s. Thus:
P = 12,000 J / 15 s = 800 W (watts).

Next, use the power formula in terms of voltage (V) and current (I), which is P = V * I. Rearrange it to solve for current:
I = P / V.
Using the power calculated above and the given voltage (230 V), we find:
I = 800 W / 230 V ≈ 3.48 A.

Therefore, the current through the coffee machine is approximately 3.48 amperes (to two significant figures).