Question

With the help of circuit diagram derive the formula for the equivalent resistance for three resistance connected in series.

Answer 1

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Answer 2

Three resistors connected in series:

The connection of the three resistors is given in the image below.

The resistors are connected in series, so, same current flows through the circuit but different potential difference.

Let I be current flowing through the circuit.

Let V be the potential difference across the circuit.

On applying Ohm's law in the each resistor, we get,

$\bold{\mathrm{V}_{1}=I\mathrm{R}_{1}}$

$\bold{\mathrm{V}_{2}=\mathrm{IR}_{2}}$

$\bold{\mathrm{V}_{3}=\mathrm{IR}_{3}}$

Now, $\bold{R_s}$ is the equivalent resistance of the three resistors.

Now, on adding all the potential differences, we get,

$\bold{V = V_1 +V_2 +V_3}$

On substituting potential difference, we get,

$\bold{\mathrm{IR}_{\mathrm{s}}=\mathrm{IR}_{1}+\mathrm{IR}_{2}+\mathrm{IR}_{3}}$

$\bold{\therefore \mathrm{R}_{\mathrm{s}}=\mathrm{R}_{1}+\mathrm{R}_{2}+\mathrm{R}_{3}}$

Thus, when the resistors are connected in series, then we need to add the resistance of the each resistor.