State Kirchhoffs rule. Apply these rules to the loops PRSP AND PRQP to write the expressions for current I1, I2, I3 in the given circuit
 

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Please find below the solution to the asked query:

Kirchhoff's current law (KCL)

The algebraic sum of currents in a network of conductors meeting at a point is zero.

Kirchhoff's voltage law (KVL)

The algebraic sum of the products of the resistance of the conductors and the currents in them in a closed loop is equal to the total emf available in that loop.

For the above loop,

If we apply the current rule at junction P, then,

$I_3=I_1+I_2$

If we apply the loop law for the loop PRSP​,

$$\begin{gathered} If we apply KVL to loop PRSP, 5=20 I_3+200 I_2 \\ For loop PRQP, 4=20 I_3+60 I_1 \\ So, 4=20 \left(I_1+I_2\right)+60 I_1\Rightarrow 4=20 I_2+80 I_1 \\ For loop PQRSP, \\ 5-4=200 I_2 - 60 I_1\Rightarrow 1=200 I_2 - 60 I_1 \\ Therefore, \\ -200 I_2 + 60 I_1=-1 \\ 200 I_2+800 I_1=40 \\ 860 I_1=39\Rightarrow I_1=\frac{39}{860}\Rightarrow I_1=45.4 mA \\ So, \\ 20 I_2=4-80 I_1\Rightarrow 20 I_2=4-80\times 0.0454 \\ \Rightarrow 20 I_2=4-3.632 \Rightarrow 20 I_2=0.368 \\ \Rightarrow I_2=18.4 mA \\ So, \\ {I}_3=I_1+I_2=45.4+18.4\Rightarrow I_3=63.8 mA \end{gathered}$$
 

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