Question

Explain with the help of a labelled circuit diagram how will you find the resistance of a combination of three resistors, of resistance R₁, R₂ and R₃ joined in parallel. Also mention how you will connect the ammeter and the voltmeter in the circuit when measuring the current in the circuit and the potential difference across one of the three resistors of the combination.

Answer 1

Applied voltage = V

Let the current in the circuit = I

If total resistance of the circuit is R_net, then

$I=\frac{V}{R_{\mathrm{net}}}$

As all the resistances are connected in parallel, so all of the resistors will get an equal voltage across their ends.

The total current in the circuit is simply the sum of the current passing through each resistance.

$$\begin{gathered} I=I_1+I_2+I_3 \\ \Rightarrow \frac{V}{R_{\mathrm{net}}}=\frac{V}{R_1}+\frac{V}{R_2}+\frac{V}{R_3} \\ \Rightarrow \frac{1}{R_{\mathrm{net}}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} \end{gathered}$$


An ammeter is low impedance device which is always connected in the series with the circuit so that maximum of the current can pass through it and it can give a more accurate value of the current flowing in the circuit.

A voltmeter is a high impedance device which is always connected in parallel in the circuit so that it does not draw any current and can give the actual voltage drop across the component.