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 

          a) Separately

          b) In series

          c) In parallel.

What is the value of the current in the three cases?

Given an electric oven with two coils,

Resistance of coil A = Resistance of coil B = 24 Ω

i.e., ${\mathrm{R}}_{\mathrm{A}}={\mathrm{R}}_{\mathrm{B}}=24 \Omega$

Voltage, V = 220 V

a) Current, ${\mathrm{I}}_1$ used when coils are used separately

According to Ohm’s law,

                                                 ${\mathrm{I}}_1=\frac{\mathrm{V}}{{\mathrm{R}}_1}$

where, ${\mathrm{R}}_1={\mathrm{R}}_{\mathrm{A}}={\mathrm{R}}_{\mathrm{B}}=24 \Omega$

Substituting the values,

                                                 ${\mathrm{I}}_1=\frac{220}{24}=9.166 \mathrm{A}$

Therefore, $9.166 \mathrm{A}$current will flow through each coil when used separately.

b) Current, ${\mathrm{I}}_2$ used when coils are connected in series

According to Ohm’s law,

                                                 ${\mathrm{I}}_2=\frac{\mathrm{V}}{{\mathrm{R}}_2}$

where, ${\mathrm{R}}_2={\mathrm{R}}_{\mathrm{A}}+{\mathrm{R}}_{\mathrm{B}}=24 \Omega +24 \Omega =48 \Omega$

Substituting the values,

                                                 ${\mathrm{I}}_2=\frac{220}{48}=4.583 \mathrm{A}$

Therefore, $4.583 \mathrm{A}$current will flow through the circuit when the coils are connected in series.

c) Current, ${\mathrm{I}}_3$ used when coils are connected in parallel

According to Ohm’s law,

                                                 ${\mathrm{I}}_3=\frac{\mathrm{V}}{{\mathrm{R}}_3}$

where, ${\mathrm{R}}_3=\frac{1}{{\displaystyle \frac{1}{{\mathrm{R}}_{\mathrm{A}}}}+{\displaystyle \frac{1}{{\mathrm{R}}_{\mathrm{B}}}}}=\frac{1}{{\displaystyle \frac{1}{24}+\frac{1}{24}}}=12 \Omega$

Substituting the values,

                                               ${\mathrm{I}}_3=\frac{220}{12}=18.33 \mathrm{A}$

Therefore, $18.33 \mathrm{A}$ current will flow through the circuit when coils are connected in parallel.