### Chapter 3: Electricity

Q
##### Electricity

Question:

A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of 24 Ω resistance, which may be used separately, in series, or in parallel. What are the currents in the three cases?

(i) When the two coils A and B are used separately.

According to Ohm’s law,

$V = IR$

$I = \frac{V}{R}$

Given: $R = 24\ \Omega , V = 220\ V$

$I = \frac{220}{24}$

$I = 9.166\ A$

(ii) When the two coils are connected in series.

Total resistance, $R = 24 + 24 = 48\ \Omega$

$V = 220\ V$ {Given}

According to Ohm’s law,

$V = IR$

$I = \frac{V}{R}$

$I = \frac{220}{48}$

$I = 4.58\ A$

(iii) When the two coils are connected in parallel.

Total resistance, $\frac{1}{R} = \frac{1}{24} + \frac{1}{24}$

$\frac{1}{R} = \frac{1 + 1}{24}$

$\frac{1}{R} = \frac{2}{24}$

$\frac{1}{R} = \frac{1}{12}$

$R = 12\ \Omega$

$V = 220\ V$ {Given}

According to Ohm’s law,

$V = IR$

$I = \frac{V}{R}$

$I = \frac{220}{12}$

$I = 18.33\ A$

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