First slide

Electrical power

Question

Two 1000 W heaters when connected in parallel across 220 V supply produce heat H_p in time t. If they are connected in series across the same power supply, the heat produced in the same time is H_S. What is (H_P / HS) ?

Moderate

A

4
B

2
C

0.5
D

0.2

Solution

Power in parallel P_p $= P_{1} + P_{2}$
Power in series $P_{S} = \{P_{1} P_{2} / (P_{1} + P_{2})\}$
We know that heat produced H = Pt
$∴ H_{P} = P_{P} \times t = (P_{1} + P_{2}) t$
and $H_{S} = P_{S} \times t = \{P_{1} P_{2} / (P_{1} + P_{2})\} t$
$\begin{array}{l} ∴ \frac{H_{P}}{H_{S}} = \frac{P_{P}}{P_{S}} = \frac{{(P_{1} + P_{2})}^{2}}{P_{1} P_{2}} \\ = \frac{2000 \times 2000}{1000 \times 1000} = 4 \end{array}$

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