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?

Answer 1

Supply voltage, $V= 220 \ V$
Resistance of one coil, $R= 24\ Ω$
Case (i): Coils are used separately
According to Ohm's law,
$V= I_1R_1$
Where,
$I_1$ is the current flowing through the coil
$I_1 = \frac {V}{R_1}$

$I_1 = \frac {220}{24}$
$I_1= 9.166 \ A$

Therefore, 9.16 A current will flow through the coil when used separately.

Case (ii): Coils are connected in series
Total resistance, $R_2 = 24 Ω + 24 Ω = 48 Ω$
According to Ohm's law, $V = I_2R_2$
Where,
$I_2$ is the current flowing through the series circuit
$I_2 = \frac {V}{R_2}$

$I_2 = \frac {220}{48}$
$I_2 = 4.58\ A$

Therefore, 4.58 A current will flow through the circuit when the coils are connected in series.

Case (iii): Coils are connected in parallel
Total resistance,
$R_3$ = $\frac {1}{\frac {1}{24}+\frac {1}{24}}$

$R_3= \frac {24}{2}$
$R_3 = 12\ Ω$
According to Ohm's law,
$V= I_3R_3$
Where,
$I_3$ is the current flowing through the circuit
$I_3 = \frac {V}{R_3}$

$I_3= \frac {220}{12}$
$I_3= 18.33\ A$

Therefore, 18.33 A current will flow through the circuit when coils are connected in parallel.