Find the currents flowing in the circuit in Figure \(21.52\). Explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors.

Figure \(21.52\)

Equation Transcription:

Text Transcription:

21.52

Solution 38PE

Apply the formula of node at point a,

I3 =I1 + I2

I1 + I2 -I3 = 0…… (1)

Apply the loop rule in loop aklefghija as follows,

40.5 I2 + 78.25 I3 = 18…… (2)

Apply the loop rule in loop abcdelka as follows,

25.1 I1 + 50.1 I2 = 24…… (3)

Now, substitute the value of I3 from equation (1) into equation (2), we get

25.1 I1 + 78.25 ( I1 + I2 ) = 18

25.1 I1 + 78.25 I1 + 78.25 I2 = 18

103.35I1 + 78.25I2 = 18…… (4)

Now, simplify the equation (4) and equation (3) and by solving the equations the value of currents is, I1 = 0.54A, I2 = -0.2057A and .I3 = 0.3365A

the current flowing in the circuit is I1 = 0.54A, I2 = -0.2057A and I3 = 0.3365A