For the circuit shown in the figure below find the following

For the circuit shown in the figure below, find the following. The current in each resistor I_1ohm = A I_2ohm(top) = A I_2ohm(middle) = A I_6 ohm = A the power supplied by each source of emf P_4V(top) = W P_4V(middle) = W P_gv = W the power delivered to each resistor P_1ohm = WP_2ohm(top) = W P_2ohm(middle) = W P_6ohm = W

Solution

suppose loop current in left loop is i1 in clockwise direction.

loop current in right side loop is i2 in clockwise direction.

Applying KVL:

8 - 1i1 + 4 - 2i1 - 2(i1-i2) - 4 = 0

5i1 - 2i2 = 8 .........(i)

on right side loop:

4 - 2(i2-11) + 6i2 = 0

-2i1 + 8i2 = 4 ......(ii)

solving these two equation,

i1 = 2 A. i2 = 1 A

I(1) = i1 = 2A

I(2 top) = i1 = 2A

I(2 middle) = i1 - i2 = 2-1 = 1 A

I(6) =i2 = 1 A

b) P= VI

P(4 top)= 4 x 2 = 8 W

P(4 middle ) = -4 x 1 = -4 W

P(8V) = 8 x 2 = 16 W

c) P = i^2 R

P(1) = 2^2 x 1 = 4W

P(2) = 8W

P(2 mid ) = 2 W

P(6) = 6 W