Question

State Kirchhoff’s second law (loop rule) as a mathematical equation, mentioning what the symbols used stand for.

Answer 1

Hint: There are two laws given by Kirchhoff for determination of potential difference and current in different branches of any complicated network. Law of conservation of charge is a consequence of the continuity equation. First law is basically junction law: the total entering is equal to the total current outgoing. This law is based on the law of conservation of charge.

Complete step by step solution:
Second law is also called loop rule or potential law. In any closed circuit the algebraic sum of all potential differences and emf is zero .$\sum\limits_{{}}^{{}}{E-\sum\limits_{{}}^{{}}{IR=0}}$ while moving from negative to positive terminal inside the cell, emf is taken positive while moving in the direction of current in a circuit the potential drop (i.e. $IR$) across resistance is taken as positive. This law is based on the law of conservation of energy.

$-{{i}_{1}}{{r}_{1}}-{{i}_{2}}{{r}_{2}}+E=0$
The change in potential in traversing a resistance in the direction of the current is $-ir$.
By applying KVL, we get one equation, but in order to solve the circuit, we require as many equations as there are unknowns. So we select the required number of loops and apply kirchhoff voltage law across each such .

Note:
After solving a set of simultaneous equations, we obtain the numerical values of the assumed currents. If any of these values comes out to be negative, it indicates that the particular current is in the opposite direction from the assumed one. While considering the voltage drop or gain across an inductor, we always assume current to be in increasing function.