A 415 Watt mercury vapour lamp was switched on for 12 hours per day. The supply volt is 220 V. Find the energy consumption per day? (Volt = 220 V, Current = 2 amps, PF = 0.85)

Solution: To find the energy consumption per day for the mercury vapor lamp, we need to calculate the power consumption per hour and then multiply it by the number of hours the lamp is operated per day.

Given:

• Power of the lamp ($𝑃$) = 415 W
• Supply voltage ($𝑉$) = 220 V
• Current ($𝐼$) = 2 A
• Power factor ($𝑃𝐹$) = 0.85
• Operating time per day = 12 hours

First, let's calculate the real power consumed by the lamp using the formula:

$\text{Real power (W)}=𝑉\times 𝐼\times 𝑃𝐹$

$\text{Real power (W)}=220\text{V}\times 2\text{A}\times 0.85$

$\text{Real power (W)}=374\text{W}$

Now, let's find the energy consumption per hour:

$\text{Energy consumption per hour (Wh)}=\text{Real power (W)}\times \text{Time (hours)}$

$\text{Energy consumption per hour (Wh)}=374\text{W}\times 1\text{hour}$

$\text{Energy consumption per hour (Wh)}=374\text{Wh}$

Finally, to find the energy consumption per day, we multiply the energy consumption per hour by the number of hours the lamp is operated per day:

$\text{Energy consumption per day (Wh)}=\text{Energy consumption per hour (Wh)}\times \text{Operating time per day (hours)}$

$\text{Energy consumption per day (Wh)}=374\text{Wh}\times 12\text{hours}$

$\text{Energy consumption per day (Wh)}=4488\text{Wh}$

So, the energy consumption per day for the mercury vapor lamp is 4488 watt-hours (Wh).