(a) Explain why in household circuits only the fuse is connected in series with all the rest of the appliances but all appliances are connected in parallel to each other.

(b) In a household circuit, an electric heater of power 1500 W and a fan of power 500 W are connected in parallel to a 220 V supply. A fuse rated for 10 A is connected to the circuit to protect it from excessive current.

1. Calculate the total current drawn by the heater and the fan.
2. Determine whether the 10 A fuse is appropriate for this circuit or if it will blow.

(a) In household circuits, the fuse is connected in series with all appliances to ensure that it can cut off the entire circuit in case of excessive current, preventing hazards like fires or damage. This way, any overload or short circuit causes the fuse to blow, protecting all appliances.
Appliances are connected in parallel to ensure each receives the same voltage from the mains and can operate independently. This setup allows appliances to work simultaneously and efficiently, with each drawing only the current it needs, without affecting others.

(b) Given,

• Power rating of the heater ($\text P_1$) = 1500 W
• Power rating of the fan ($\text P_2$) = 500 W
• Supply voltage ($\text V$) = 220 V
• Current rating of the fuse ($\text I$) = 10 A

(a) Let, current passing through the heater be $\text I$1 and through the fan is $\text I2$.

Then,

$\text I$1 = \dfrac{\text P1}{\text V} \\[1em] = \dfrac{1500}{220} \\[1em] = \dfrac{150}{22} \\[1em] = \dfrac{75}{11} \\[1em] \Rightarrow \text I_1 \approx 6.82\ \text A

Similarly,

$\text I$2 = \dfrac{\text P2}{\text V} \\[1em] = \dfrac{500}{220} \\[1em] = \dfrac{50}{22} \\[1em] = \dfrac{25}{11} \\[1em] \Rightarrow \text I_2 \approx 2.27\ \text A

Total current drawn by the heater and the fan = $\text I$1 + \text I2 = 6.82 + 2.27 = 9.09 A

Hence, the total current drawn by the heater and the fan is about 9.09 A.

(b) As, I > 9.09 A

Since 9.09 A < 10 A, the fuse will not blow and is appropriate for this circuit, as the total current is within the fuse’s capacity.