current-electricity Question 41
Question: Q. 1. State Kirchhoff’s rules. Explain briefly how these rules are justified. R [Delhi I, II, III 2014]
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Solution:
Ans. Kirchhoff’s first law is known as junction rule which states that for a given junction or node in a circuit, sum of the currents entering will be equal to sum of currents leaving.
Kirchhoff’s second law is also known as loop rule which shows that around any closed loop in a circuit, sum of the potential differences across all elements will be zero
Justification : The junction rule is in accordance with the conservation of charge that serves as basis of current rule while loop rule is based on law of conservation of energy.
[CBSE Marking Scheme 2014]
[AI Q. 2. Use Kirchhoff’s rules to obtain conditions for the balance condition in a Wheatstone bridge.
A [Delhi I, II, III 2015]
Ans. Applying Kirchhoff’s loop rule to closed loop ADBA
For loop $C B D C$,
$-I_{2} R_{4}+I_{8} R_{G}+I_{1} R_{3}=0 \quad\left(I_{g}=0\right)$
from equation (i)
$$ \frac{I_{1}}{I_{2}}=\frac{R_{2}}{R_{1}} $$
From equation (ii)
$$ \begin{array}{rlrl} & \frac{I_{1}}{I_{2}} & =\frac{R_{4}}{R_{3}} \ & \therefore & \frac{R_{1}}{R_{2}} & =\frac{R_{3}}{R_{4}} \ \text { or, } & \frac{P}{Q} & =\frac{R}{S} \end{array} $$
