A.) Write Kirchoff\'s rules for two loops and one junction in the circuit in Fig

Question

A.) Write Kirchoff's rules for two loops and one junction in the circuit in Figure P16.39.

B.) Solve the equations for the current.

C.) Determine the potential differnce across resistor R3 from point B to point A.

equations for the current in Figure P16.39 each branch of the circuit when R, = 200 , and R3 = 2012. ference across resistor R, from (c) Determine the potential dif- A point B to point A. 40. BIO Electric eel The South Figure P Figure P16.40 American eel can generate c current that can stun nearby fish. Thei ows of Electric eel 750 V 1 5 750 V

Explanation / Answer

Let current in resistor R1 is I1 and R2 is I2 and R3 is I3.

Now from junction law, I1 = I2 +I3

In the loop through R1 and R3, with voltage law we have,

-I1R1 -I3 R3 +E1 = 0

For bigger loop

-I1R1 -I2R2 +E2 +E1 = 0

Now substitute I1 = I2 +I3

E1 = I2 R1 + I3 (R1 + R3)

E2+E1 = I2 (R1+R2) +I3 R1

Solving gives I2 = (E1 R3 + E2 R1 + E2 R3)/ ( R1 R2 +R2 R3 +R1 R3)

I3 = (E1 R2 -E2 R1) / ( R1 R2 +R2 R3 +R1 R3)

I1 = (E1 ( R2 + R3) +E2 R3) / ( R1 R2 +R2 R3 +R1 R3)

Potential difference across R3 is I3R3

Which is R3 (E1 R2 -E2 R1) / ( R1 R2 +R2 R3 +R1 R3)

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