Deal with the following figure. In each, let the total current be equal to I, th

Question

Deal with the following figure. In each, let the total current be equal to I, the current through the 10 Ohm resistor be I_2, the current tlirough the 6 Ohm resistor be I_3 and the currents through the 8 Ohm and 4 Ohm resistors be I_4 and I_5 respectively. 4. Using Kirchoff's law of currents, find the expressions for current conservation. 5. Using Kirchoff's law for voltage loops, write down the expressions for each of the three loops that current can take. 6. Using these expressions, find each of the four currents in the circuit. Compare your result to Problem 5 in the last homework set. Do your results agree?

Explanation / Answer

4)
Using Kirchoff Current law,
I = I2 + I3
I3 = I4 + I5

5)
Using Kirchoff Voltage law,
I*0.5 + I2*10 + I*5.0 = 9.0
I * 5.5 + I2 * 10 = 9.0

I2 * 10 = I3 * [6 + (8*4)/(8+4) ]
I2 * 10 = I3 * 8.67

8.0 * I4 = 4.0 * I5
2.0 * I4 = I5

(6)
Req = 0.5 + 5.0 + (8.67*10.0)/(8.67 + 10.0)
Req = 10.14

V = I* Req
I = 9.0/10.14
I = 0.887 A

Solving the eq,

I2 = 0.41 A
I3 = 0.475 A

0.475 = 3.0 * I4
I4 = 0.158 A

I5 = 0.316 A

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