How do you solve the answer to question 3 and 4?
(B.) Two parallel rails with negligible resistance are 12.0 cm apart and are connected by a resistor of resistance R3 = 5.00 Ω. The circuit also contains two metal rods having resistances of R1 = 10.5 Ω, and R2 = 15.00 Ω sliding along the rails (see figure). The rods are pulled away from the resistor at constant speeds of v1 = 4.00 m/s and v2 = 2.00 m/s. A uniform magnetic field of magnitude B = 0.0100 T is applied perpendicular to the plane of the rails. Determine the current in R3, in A.
Note: This is both an "induced/motional emf problem and a "Kirchhoff's Law" problem.
X + x x x x x x x
X
X
x X xB;x x
x
X x x
x
V.
Consider the two outside loops separately:
a. What is the direction of the induced current through each rod? (Use Lenz's law!) Label these currents I1 and I2 respectively.
Rg x x +
x
X
X
x
R1
R2
b. If you were to model the induced emf as a battery, in what orientation would you place a battery on each of the two rods to produce the currents from part (a)? (That is, on which side (top or bottom) would the positive terminal of the battery be?) Re-draw this as a circuit with two batteries, E1 and E2, along with resistors R, R1, and R2 by completing the circuit depicted below. Add arrows indicating direction on the currents: I1, I2, and I3 (where I3 is through the central section and R3).
12 R,
R
R3
E1
E2
c. Determine the magnitude of the induced emf through each outside loop: E1 and E2. (Use Faraday's Law and our example "motional emf" problem.)
d. Use Kirchhoff's Laws and your circuit diagram from part (b) to solve for the current through R3, in A. (3.) [0.99 point] I3 = A (4.) [0.41 point] What is the direction of I3 through R3? a. Upward b. Downward
