In the circuit of the figure below determine the current in

In the circuit of the figure below, determine the current in each resistor and the potential difference across the R = 350- resistor.

(a) the current in each resistor

(b) the potential difference across the R = 350- resistor
V

Solution

Assumption:

There are four loops:

Small loops L1, L2 and L3

bigger loop L4

current through 350 ohm is I1

current through 80 ohm is I2

current through 20 ohm is I3

current through 70 ohm is I4

Current through junction of 80 and 20 ohm is I5

Applying Kirchoff\'s Loop Rule:

At junction 1 below 80 ohm:

I1 + I2 = I5

At junction 2 below 20 ohm:

I5 + I3 + I4 = 0

which gives

I1 + I2 + I3 + I4 = 0 (1)

in loop 1

-40 V = I2*80 - I1*350 (2)

in loop 2

40 + 360 = I3*20 - I2*80 (3)

in loop 3

-360 - 80 = I4*70 - I3*20 (4)

in loop 4

80 = I4*70 - I1*350 (5)

Now we have 5 equation and 4 unknown

Solving these equations:

I1 = -0.586 Amp.

I2 = -3.067 Amp.

I3 = 7.73 Amp.

I4 = -4.076 Amp.

B.

Voltage through 350 ohm

V = IR

V = 0.586*350 = 205.1 V

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