An electric heater of 220 V, 2 kW rating is used for hot water generation in an industry. Find electricity consumption per hour (a) at the rated voltage (b) at 200 V.

 Solution: To find the electricity consumption per hour for the electric heater, we'll use the power rating and the given voltages.

Given:

• Voltage ($𝑉$) of the heater = 220 V
• Power rating ($𝑃$) of the heater = 2 kW (or 2000 W)

(a) At the rated voltage (220 V):

To find the electricity consumption per hour at the rated voltage, we use the formula for power:

$𝑃=𝑉𝐼$

Where:

• $𝑃$ is the power (2000 W),
• $𝑉$ is the voltage (220 V),
• $𝐼$ is the current.

We can rearrange this formula to solve for current ($𝐼$):

$𝐼=\frac{𝑃}{𝑉}$

Plugging in the given values:

$𝐼=\frac{2000\text{W}}{220\text{V}}$

$𝐼\approx 9.09\text{A}$

Now, to find the electricity consumption per hour, we multiply the power by the time (in hours):

$\text{Electricity consumption per hour}=𝑃\times \text{Time}$

Given that the time is 1 hour:

$\text{Electricity consumption per hour}=2000\text{W}\times 1\text{hour}$

$\text{Electricity consumption per hour}=2000\text{Wh}$

(b) At 200 V:

To find the electricity consumption per hour at 200 V, we'll use the same power rating (2000 W) and the new voltage (200 V). Using the same approach as above:

$𝐼=\frac{2000\text{W}}{200\text{V}}$

$𝐼=10\text{A}$

Now, for electricity consumption per hour:

$\text{Electricity consumption per hour}=2000\text{W}\times 1\text{hour}$

$\text{Electricity consumption per hour}=2000\text{Wh}$

So, regardless of the voltage, the electricity consumption per hour remains 2000 watt-hours (Wh) for the given 2 kW-rated electric heater.