Question

Give the law of combination of resistances in series.

Answer 1

Hint: Use the formula of the ohm law and find the potential difference across each resistor, from that find the total potential difference across the circuit. Derive the equal resistance across the circuit from the derived potential difference.

Useful formula:
The ohm’s law is given by
$V = IR$
Where $V$ is the potential difference across the resistance, $I$ is the current flowing through the circuit and $R$ is the resistance in the circuit.

Complete step by step solution:
Let us construct the circuit diagram in which the three resistors are connected in series. Since the resistors are connected in series, all the resistors have equal current flowing through them but their potential difference varies for each resistor connected in the circuit.

${V_1} = I{R_1}$
${V_2} = I{R_2}$
${V_3} = I{R_3}$
Let us add all the three potential differences to find the total potential difference developed in the circuit.
$V = {V_1} + {V_2} + {V_3}$
Substituting their parameters in the above equation, we get
$V = I{R_1} + I{R_2} + I{R_3}$
Since the current is same in all the three resistors,
$V = I\left( {{R_1} + {R_2} + {R_3}} \right)$ ……………………………………..(1)
For the full circuit, the ohm’s law is substituted as follows.
$V = I{R_{eq}}$ ……………………………………….(2)
Comparing the equation (1) and (2), we get
${R_{eq}} = {R_1} + {R_2} + {R_3}$
Hence the equivalent resistance is the sum of the resistance of the individual resistors connected in series. This is called by the name law of the combination of resistances in series.

Note: Remember that in a series circuit, the current flows through each resistor will be the same and the voltage and the resistance of the total circuit will be equal to the sum of the individual parameters. Parallel circuit is opposite to a series, in which the voltage is the same across the circuit and the current will be the sum of the current through the individual circuits.