An electric heater consumes 2.3 MJ when connected to a 220 V supply for 45 minutes. Find the power rating of the heater and the current taken from the supply?

Solution: 

To find the power rating of the heater and the current taken from the supply, we can use the formulas relating power, energy, voltage, current, and time.

First, let's find the power rating ($𝑃$) of the heater. Power is the rate at which energy is consumed, so we can use the formula:

$𝑃=\frac{𝐸}{𝑡}$

where:

• $𝐸$ is the energy consumed (2.3 MJ = $2.3\times 10^6$ J),
• $𝑡$ is the time (45 minutes = 45 × 60 seconds).

$𝑃=\frac{2.3\times 10^6\text{J}}{45\times 60\text{s}}$

$𝑃=\frac{2.3\times 10^6\text{J}}{2700\text{s}}$

$𝑃=851.85\text{W}$

Now, let's find the current ($𝐼$) taken from the supply. We can use Ohm's law:

$𝑃=𝑉𝐼$

where:

• $𝑉$ is the voltage (220 V),
• $𝐼$ is the current.

We already found $𝑃=851.85\text{W}$, so let's rearrange the formula to solve for $𝐼$:

$𝐼=\frac{𝑃}{𝑉}$

$𝐼=\frac{851.85\text{W}}{220\text{V}}$

$𝐼\approx 3.87\text{A}$

So, the power rating of the heater is approximately $851.85\text{W}$ and the current taken from the supply is approximately $3.87\text{A}$.