Answer to Question #118792 in Electric Circuits for Ceejay

Question

A restaurant uses five 80% energy efficient 30 W bulbs, a refrigerator marked “240 V, 5A” and a 1.5
kW electric cooker. These loads are connected to 220 V mains supply. The bulbs, refrigerator and
electric cooker are switch on for 12 hours, 24 hours and 5 hours respectively on daily average. The
restaurant opens six days a week – all loads are switched off throughout the 7th day.
(a) Determine the resistance of the refrigerator.
(b) (i) Calculate the electrical power in the refrigerator when plugged to the 220 V power outlet.
(ii) Calculate the input power of each light bulb.
(iii) At what rate is energy consumed by the restaurant?
(c) If the restaurant needs a single fuse to protect all its devices, recommend the rating of the fuse in
amperes.
(d) Calculate the daily energy consumption of the restaurant.
(e) If PHCN charges ₦32 per kWh, calculate the monthly (4 weeks) bill.

Answer 1

(a) Determine the resistance of the refrigerator:

$$R=\frac{V}{I}=\frac{240}{5}=48\space\Omega.$$

(b) (i) Calculate the electrical power in the refrigerator when plugged to the 220 V power outlet:

$$P_r=\frac{V^2}{R}=\frac{220^2}{48}=1000\text{ W}.$$

(b) (ii) Calculate the input power of each light bulb:

$$P_b=\frac{P_\text{rated}}{\eta}=\frac{30}{0.8}=37.5\text{ W}.$$

(b) (iii) At what rate is energy consumed by the restaurant?

The rate of energy consumption is energy per unit time, or power:

$$P_\text{total}=5\cdot37.5+1000+1500=2690\text{ W}.$$

(c) If the restaurant needs a single fuse to protect all its devices, recommend the rating of the fuse in amperes is

$$I=\frac{P_\text{total}}{V}=\frac{2690}{220}=12.2\text{ A}.$$

(d) Calculate the daily energy consumption of the restaurant.

The bulbs work 12 h, refrigerator works 24 h, electric cooker works 5 hours a day:

$$E=5P_bt_b+P_rt_r+P_ct_c=\\ =5\cdot\frac{37.5}{1000}\cdot12+1\cdot24+1.5\cdot5=33.8\text{ kWh}.$$

(e) If PHCN charges ₦32 per kWh, calculate the monthly (4 weeks) bill.

The restaurant works six days a week, there are 4 weeks (24 days) in a month, the monthly bill is

$$B_m=NEc=24\cdot33.8\cdot32=25958\text{ ₦/month}.$$