Question

A hot plate of an electric oven connected to $220V$ line has two resistance coils A and B, each of $22\Omega$ resistance, which may be used separately, in series or in parallel. What are the currents in three cases?

Answer 1

Step 1 - Given data

$$\begin{gathered} R_1=22\Omega \\ {R}_2=22\Omega \\ V=220V \end{gathered}$$

Step 2 - Finding current in a separate case.

Assume $i$ current is flowing through $R_1$. Now according to Ohm's law, $i=\frac{V}{R_1}$.

Substitute the values given into the formula of $i$ to calculate the current through the resistance.

$$\begin{gathered} i=\frac{220V}{22\Omega } \\ =10A \end{gathered}$$

As both of the resistors have resistances, so the amount of current when they are used separately, will have the same value of current through them.

Step 3 - Finding the equivalent resistance of the series combination.

Assume the equivalent resistance, for the series combination, is $R_{eq}$. The formula to calculate the equivalent resistance is given by $R_{eq}=R_1+R_2$. Substitute the values into the formula to calculate the equivalent resistance in a series combination.

$$\begin{gathered} R_{eq}=22\Omega +22\Omega \\ =44\Omega \end{gathered}$$

Step 4 - Finding the current flow in a series circuit.

Assume the current flowing through the circuit is $i_s$. According to Ohm's law, the formula to calculate current is given by $i_s=\frac{V}{R_{eq}}$. Substitute the values into the formula of $i_s$ to calculate the current flowing through the series combination.

$$\begin{gathered} i_s=\frac{220V}{44\Omega } \\ =5A \end{gathered}$$

Step 5 - Finding the equivalent resistance of parallel combination.

Assume the equivalent resistance, for the parallel combination is $R_{eq\text{'}}$. The formula to calculate the equivalent resistance is given by $\frac{1}{R_{eq\text{'}}}=\frac{1}{R_1}+\frac{1}{R_2}$. Substitute the values into the formula to calculate the equivalent resistance in a parallel combination.

$$\begin{gathered} \frac{1}{R_{eq\text{'}}}=\frac{1}{22\Omega }+\frac{1}{22\Omega } \\ \frac{1}{R_{eq\text{'}}}=\frac{1+1}{22\Omega } \\ {R}_{eq\text{'}}=\frac{22\Omega }{2} \\ {R}_{eq\text{'}}=11\Omega \end{gathered}$$

Step 6 - Finding the current flow in the parallel circuit.

Assume the current flowing through the circuit is $i_p$. According to Ohm's law, the formula to calculate current is given by $i_p=\frac{V}{R_{eq}\text{'}}$. Substitute the values into the formula of $i_p$ to calculate the current flowing through the parallel combination.

$$\begin{gathered} i_p=\frac{220V}{11\Omega } \\ =20A \end{gathered}$$

Final answer -

• When the resistances are used separately then the amount of current flowing through both of them is the same that is $10A$.
• When they are in series combination then the current flowing through the circuit is $5A$.
• Finally when the resistances are in parallel combination then the current flowing through the circuit is $20A$.