Question

An establishment receives electric energy at a rate of ₹ 4.50 per kWh at a p.d of 240 V. It uses the following appliances:

1. 20 tube lights of 40 W each working 10 h a day.
2. Two stereo systems, each drawing a current of 2A and working 4h a day.
3. Four ovens, each of resistance 24 Ω working 6 h a day.
4. Two cooling machines of 4 H.P each working 15 hours a day.
   1. Calculate the monthly bill
   2. Minimum fuse rating of the circuit

Answer 1

(a) Power of 20 tube lights \[ = 20 \times 40 \] \[ = 800 \text{ W} \]

∴ Energy consumed by the tube lights in a day \[ = 800 \text{ W} \times 10 \text{ h} \]

\[ = 8000 \text{ Wh} \]

\[ = 8 \text{ kWh} \]

(b) Power of one stereo system \[ = V \times I \]

\[ = 240 \times 2 \]

\[ = 480 \text{ W} \]

∴ Power of 2 stereo systems \[ = 2 \times 480 \] \[ = 960 \text{ W} \]

∴ Energy consumed by the stereo systems in a day \[ = 960 \text{ W} \times 4 \text{ h} \]

\[ = 3840 \text{ Wh} \]

\[ = 3.84 \text{ kWh} \]

(c) Power of one oven \[ = \frac{V^2}{R} \]

\[ = \frac{240 \times 240}{24} \]

\[ = \frac{57600}{24} \]

\[ = 2400 \text{ W} \]

∴ Power of 4 ovens \[ = 4 \times 2400 \] \[ = 9600 \text{ W} \]

∴ Energy consumed by the ovens in a day \[ = 9600 \text{ W} \times 6 \text{ h} \]

\[ = 57600 \text{ Wh} \]

\[ = 57.6 \text{ kWh} \]

(d) Power of one cooling machine \[ = 4 \times 750 \] \[ = 3000 \text{ W} \]

∴ Power of 2 cooling machines \[ = 2 \times 3000 \] \[ = 6000 \text{ W} \]

∴ Energy consumed by the cooling machines in a day \[ = 6000 \text{ W} \times 15 \text{ h} \]

\[ = 90000 \text{ Wh} \]

\[ = 90 \text{ kWh} \]

(i) Total energy consumed in a day \[ = 8 + 3.84 + 57.6 + 90 \] \[ = 159.44 \text{ kWh} \]

∴ Total energy consumed in one month \[ = 159.44 \times 30 \] \[ = 4783.2 \text{ kWh} \]

∴ Monthly bill \[ = 4783.2 \times 4.50 \] \[ = \text{₹ } 21524.40 \]

(ii) Total power of appliances \[ = 800 + 960 + 9600 + 6000 \] \[ = 17360 \text{ W} \]

∴ Minimum fuse rating \[ = \frac{P}{V} \]

\[ = \frac{17360}{240} \]

\[ \approx 72.33 \text{ A} \]