Question

Explain the sign convention of Kirchhoff’s second law.

Answer 1

Hint: Kirchhoff’s second law is also known as Kirchhoff’s voltage law (KVL). It follows the law of conservation of charge and law of conservation of energy. The voltage drop across different points in a circuit can be known by using Kirchhoff’s voltage law.

Complete solution:
Step I: According to Kirchhoff’s second law:
The sum of all the voltages around a closed loop in any circuit will be equal to zero. This means that the net electromotive force around the loop is equal to the sum of individual potential drop across different points in the loop. According to this law:
If the charge is moving in a closed loop in the circuit, then the gain in energy and the loss of energy should be equal through the resistance.
The total voltage in any closed loop is mathematically then written as:
\[\sum V = 0\]

Step II: Sign conventions of Kirchhoff’s second law:
If the current flows from negative terminal to the positive terminal in the circuit, then the e.m.f of the battery is positive otherwise negative.
The potential difference in the circuit is negative, if the electric current crosses the resistors.

Note: It is important to remember that the Kirchhoff’s voltage law is applicable only when the magnetic field in the circuit does not fluctuate. But in case of fluctuating magnetic fields in the circuit, this law can not be applied. Also the electric energy that is gained in a closed circuit, is also lost within the same loop of the circuit.