Consider the circuit shown in the figure below Assume R1 14

Consider the circuit shown in the figure below. (Assume R_1 = 14.5 omega and R_2 = 1.00 omega Find the potential difference between points a and b. Find the current in the 20.0-omega resistor

Solution

for left loop of the circuit:

25 - I1R1 - IR1 = 0

I+I1 = 25 /R1 = 25/14.5 = 1.724 A ........ (1)

for middle loop of the circuit:

R2I2 = R1I1

I2 = [R1/R2]I1

= [14.5/4]I1

= [3.625]I1 .......(2)

for right loop of the circuit:

R2I2 = [R2+20][I-I1-I2]

4I2 = [34.5] [I-I1-I2]

(4)I2 = (34.5) I-(34.5) I1-(34.5) I2

(4)[ [3.625]I1] = (34.5) I-(34.5) I1-(34.5) [ [3.625]I1]

14.5*I1= (34.5) I - 159.5625]*I1

I = [5.045]I1

From equation (1),

  I+I1 = 1.724

   [5.045]I1 + I1 = 1.724

I1 = 0.285 A

Current I is, I = 1.724 - 0.285 = 1.439 A

From equation (2):

I2 =  [3.625][0.285] = 1.033 A

Potential difference:

V = I1R1 = 0.285*14.5 = 4.1325 V = 4.13 V

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Current in the 20 Ohms resistor is,

I₂₀ = I-I1-I2

= 1.439 - 0.285 - 1.033

= 0.121 A