Question

Draw a circuit diagram of an electric circuit containing a cell, a key, an ammeter, a resistor of $2\Omega$ in series with a combination of two resistors ($4\Omega$ each) in parallel and a voltmeter across the parallel combination. Will the potential difference across the $2\Omega$ resistor be the same as that across the parallel combination of $4\Omega$ resistors? Give reason.

Answer 1

Step 1: Given data

Resistors, $R_1=2\Omega$

$R_2=R_3=4\Omega$

Step 2: Circuit diagram

The circuit diagram can be obtained as

Step 3: Calculation of equivalent resistance

The equivalent resistance of two $4\Omega$ resistors in parallel, $R_p$, can be obtained as,

$\frac{1}{R_p}=\frac{1}{R_2}+\frac{1}{R_3}=\frac{1}{4}+\frac{1}{4}=\frac{1}{2}$

Therefore, $R_p=2\Omega$

Step 4: Calculation of potential differences

1. We now have $R_1$and $R_p$ in series.
2. For series connection, current $I$ flowing through both the resistors is the same.
3. From Ohm's law, potential difference, $V$∝$R$.
4. Since resistances are equal, therefore, the potential difference across $R_1$and $R_p$ are the same.

Hence, the potential difference across the $2\Omega$ resistor will be the same as that across the parallel combination of $4\Omega$ resistors