Consider the circuit shown in the figure Figure 1 The value

Consider the circuit shown in the figure (Figure 1) . The values of the different components are as follows:

R₁= 5 ?

R₂= 15 ?

R₃= 60 ?

?battery = emf = 9.0 Volts

r (internal resistance of the battery) = 1.5 ?

Use Kirchoff\'s rules to calculate I₁, I₂, and I₃.

switch battery R, R2 R, 3

Solution

Ans) Let the internal Resistance of battery be R=1.5 ohms

and Given R1=5 ohms ,R2=15 ohms,R3=60 ohms

Battery EMF V=9 V

Using KVL around the loop consists of R ,R1 R2

V=I1R+I2(R1+R2)

9=(1.5)I1+20(I2)------eq1

Now KVL around R ,R3 gives

V=I1R+I3R3

9=1.5(I1)+60(I3)

Using KCL I1=I2+I3

I3=I1-I2

substituting in above equation gives

9=1.5(I1)+60(I1-I2)

9=61.5(I1)-60(I2)--------eq2

9=(1.5)I1+20(I2)------eq1

solving equation 1 and 2 we get

I1=0.545 A

I2=0.409 A

I3=I1-I2=0.545-0.409=0.136 A

I3=0.136 A