Question

Question 13
A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of $24\Omega$ resistances, 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, $R=24\Omega$
(i) Coils are used separately
According to Ohm's law, $V=I_1{R}_1$
Where, $I_1$ is the current flowing through the coil
$I_1=\frac{V}{R_1}=\frac{220}{24}=9.166A$
Therefore, 9.16 A current will flow through the coil when used separately.
(ii) Coils are connected in series
Total resistance, $R_2=24\Omega +24\Omega =48\Omega$
According to Ohm's law, $V=I_1{R}_2$
Where, $I_2$ is the current flowing through the series circuit
$I_2=\frac{V}{R_2}=\frac{220}{48}=4.58A$
Therefore, 4.58 A current will flow through the circuit when the coils are connected in series.
(iii) Coils are connected in parallel
Total resistance, $R_3=\frac{1}{\frac{1}{24}+\frac{1}{24}}=\frac{24}{2}=12\Omega$
According to Ohm's law, $V=I_3{R}_3$
Where, $I_3$ is the current flowing through the circuit $I_3=\frac{V}{R_3}=\frac{220}{12}=18.33A$
Therefore, 18.33 A current will flow through the circuit when coils are connected in parallel.