Question

Please show work clearly. Thank you

16. (15 points extra credit) Two very long solenoids cross the plane of the circuit in the diagram below. The radius of the top solenoid is 15 cm and that of the bottom solenoid is 25 cm. The currents is increasing at a rate of in the solenoid windings are changing such that the magnitude of the B-field is increasing at a rate o 55.0 T/s in both solenoids. The resistances are w R1 = R3 = 42 R2=802 Loop 1 The two loops are drawn in for applying Kirchhoff's Rules; they are not physical wires and do not necessarily indicate the actual direction of current flow. a). (5 pts) Calculate the induced EMFs in the top and bottom halves of the circuit. X X X Loop 2 b) (5 pts) Write down Kirchhoff's Junction and Voltage Loop Rules for the circuit. For the Voltage Loop Rules, use loops 1 and 2 and the directions of the currents 11, 12, and 13 as drawn in the diagram. Note that the sum of the voltage drops around each loop will not be zero, but must be equal to the induced EMF in the loop.

Answer 1

(A) induced emf = rate of change on magnetic flux

e1 = (pi 0.15^2)(55 T/s)

e1 = 3.89 Volt .....Ans

e2 = (pi 0.25^2) (55 T/s)

e2 = 10.8 Volt ....Ans

(B) Junction rule,

I1 + I3 = I3

I1 - I2 + I3 = 0 .... (i)

voltage loop rules,

e1 - I1 R1 - R2 I2 = 0

4I1 + 8I2 = 3.89 ..... (ii)

and

8I2 + 4I3 = 10.8 ..... (iii)

(C) solvning,

I1 = - 0.50 A

I2 = 0.73 A

I3 = 1.23 A