Question

a) Apply the junction rule to the junction labeled with the number1 (at the bottom of the resistor of resistance $R_2$ ).

Answer in terms of given quantities,together with the meter readings $I_1$ and $I_2$ and the current $I_3$ .

b) Apply the loop rule to loop 2 (the smaller loop on the right).Sum the voltage changes across each circuit element around thisloop going in the direction of the arrow. Remember that the currentmeter is ideal.

Express the voltage drops in terms of $V_b$ , $I_2$ , $I_3$ , the given resistances, and any other givenquantities.

c) Now apply the loop rule to loop 1(the larger loop spanning the entire circuit). Sum the voltagechanges across each circuit element around this loop going in thedirection of the arrow.

Express the voltage drops in terms of $V_b$ , $I_1$ , $I_3$ , the given resistances, and any other givenquantities.

Answer 1

Concepts and reason

The given problem can be solved by using the concept of Kirchhoff’s current law and Kirchhoff’s voltage law.

Use the Kirchhoff’s law in loop 1 and 2 and find out the equation for net current and voltage.

Fundamentals

There are two rules or laws given by Kirchhoff in relation to general electric circuits. These rules or laws are called as Kirchhoff rules.

Kirchhoff’s current rule or Junction rule states that in an electric circuit the sum of currents entering a junction must equal to the sum of currents leaving the junction i.e. algebraic sum of currents entering or leaving a junction is zero. As a convention, the current entering the junction is taken as positive while current leaving the junction is taken as negative.

It can be expressed mathematically as,

$\sum I = 0$

Kirchhoff’s loop rule or voltage rule states that while traversing a closed loop in a circuit the algebraic sum of all the potentials differences is zero. As a convention, while traversing the loop, the currents which are in the direction of traversing, their potential difference is taken as negative and vice versa.

It can be expressed mathematically as,

$\sum {} V = 0$

(a)

The following figure shows the given circuit diagram.

The junction rule describes the conservation of current and charge.

(a)

The current expression at junction labeled with number 1 by Kirchhoff’s current rule is given as follows:

$\begin{array}{l}\\\sum I = 0\\\\{I_2} + {I_3} - {I_1} = 0\\\end{array}$

(b)

The voltage equation in loop 2 by Kirchhoff’s voltage rule is given as follows:

$\begin{array}{c}\\\sum V = 0\\\\ - {I_3}{R_3} + {I_2}{R_2} = 0\\\end{array}$

[Part b]

(c)

The Kirchhoff’s voltage equation for loop 1 is given as follow:

$\begin{array}{c}\\\sum V = 0\\\\ - {V_b} + {I_1}{R_1} + {I_3}{R_3} = 0\\\end{array}$

Ans: Part a

The junction rule at junction gives the expression: ${I_2} + {I_3} - {I_1} = 0$ .

Part b

The loop rule through loop 2 gives the expression: $- {I_3}{R_3} + {I_2}{R_2} = 0$ .

Part c

The loop rule through loop 1 gives the expression: $- {V_b} + {I_1}{R_1} + {I_3}{R_3} = 0$ .