Question

The junction rule describes the conservation of which quantity? Note that this rule applies only to circuits that are in a steady-state.

is it current, voltage or resistance

>Apply the junction rule to the junction labeled with the number 1 (at the bottom of the resistor of resistance R₂).

Answer in terms of given quantities, together with the meter readings I₁ and I₂ and the current I₃.

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

Express the voltage drops in terms of V_b, I₂ , I₃ , the given resistances, and any other given quantities.

>Now apply the loop rule to loop 1 (the larger loop spanning the entire circuit). Sum the voltage changes across each circuit element around this loop going in the direction of the arrow.

Express the voltage drops in terms of V_b, I₁ , I₃ , the given resistances, and any other given quantities.

Answer 1

Concepts and reason

The main concepts used to solve the problem are Kirchhoff’s current law and Kirchhoff’s voltage law.

Initially, use the circuit diagram to identify the junctions. Later, use the Kirchhoff’s current rule to calculate the current. Finally, use the Kirchhoff’s voltage rule to calculate the 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,

$\sum {} V = 0$

Consider the given circuit diagram as,

The junction rule describes the conservation of current and charge.

At junction labeled with number 1, by Kirchhoff’s current rule,

It can be expressed mathematically as,

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

In loop 2 in counterclockwise direction as shown by arrow, by Kirchhoff’s voltage rule,

It can be mathematically expressed as,

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

In the loop 1 in clockwise direction as shown by arrow, by Kirchhoff’s voltage rule,

It can be mathematically expressed as,

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

Ans:

The junction rule describes the conservation of current at a junction in the circuit.

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

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

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