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.