Question

Two resistors X and Y of resistances $2\text{ohm}$ and $3\text{ohm}$ respectively are first joined in parallel and then in series. In each case, the voltage supplied is $5\text{V}$.

(i) Draw the circuit diagram to show the combination of resistors in the parallel connection.

(ii) Calculate the voltage across the $3\text{ohm}$ resistor in the series combination of resistors.

Answer 1

(i)

The circuit diagram in case of parallel connection

(ii)

Step 1: Calculation of equivalent resistance in series connection

In a series connection, the equivalent resistance can be calculated by adding the resistances.

$$\begin{gathered} R_{eq}=2\text{ohm}+3\mathrm{ohm} \\ {R}_{eq}=5\mathrm{ohm} \end{gathered}$$

Here, $R_{eq}$is the equivalent resistance.

Step 2: Calculation of current flowing through the circuit

Since the connection is in series, the current flowing through the circuit will be the same.

$I=\frac{V}{R_{eq}}$

Here, $I$ is the current flowing in the circuit and $V$ is the voltage.

$$\begin{gathered} I=\frac{5\mathrm{V}}{5\mathrm{ohm}} \\ I=1\mathrm{A} \end{gathered}$$

Step 3: Calculation of the voltage across the $3\text{ohm}$ resistor

$$\begin{gathered} V_{3\mathrm{ohm}}=I\times 3\mathrm{ohm} \\ {\mathrm{V}}_{3\mathrm{ohm}}=1\mathrm{A}\times 3\mathrm{ohm} \\ {\mathrm{V}}_{3\mathrm{ohm}}=3\mathrm{V} \end{gathered}$$

Hence, the voltage across the $3\text{ohm}$ resistor is $3\mathrm{V}$.