Question

Using kirchhoff's rules calculate the current in the arm ac of the given circuit

Answer 1

The current through the loop I3 is 22/13 A.

Explanation:

Correct statement:

a) use kirchhoff's rules , calculate the current in the arm AC of the given circuit.

Applying kirchoff's junction rule at A node:

I3 = I1 +  I2  ......(1)

Applying kirchoff's second rule in loop EFCA:

−30 I1 + 40 − 40 I3 = 0

3I1 + 4I3 = 4 .....(2)

In loop EFDB:

−30I1 + 20 I2 − 80

= 0 − 3I1 + 2I2 = 8 .....(3)

from equation (1) put the value of I3 in equation (2).

3I1 + 4(I1 + I2) = 47I1 + 4I2 = 4  .....(4)

From (3) and (4)

13I1 = −12

I1 = −12 / 13 A

Put I1 in equation (4)

7 × −12 / 13 + 4I2 = 4

4I2 = 4 + 84 / 13

I2 = 34/ 13 A

From equation (1).

I3  = −12 / 13 + 34 / 13

I3=22 / 13 A

Thus the current through the loop I3 is 22/13 A.