Question

The following questions refer to the figure below. At the start, the switch between points c and d is open as drawn on the figure. The battery is 5 V. At this time (switch open) the current measured at point a is 5 ma, and there is a 3 V difference between a and b. R2 is larger than R3.

(A) What is the current at point d?
(B) What is the voltage between points b and d?
(C) What is the voltage between points b and c?
(D) What is the effective resistance of the circuit?
(D) If the switch is closed, explain what happens to the current at point a. (You don’t need to do any calculations.)

Answer 1

Net Req of the figure = R1 + R3 [ when the switch is open ]
I = V/Req = 5/(R1 + R3) = 5mA ...... (1)
also, IR1 = 3
5*10^-3 * R1 = 3
R1 = 600 ohm
from 1
5*10^-3 = 5/(600 + R3)
10^-3 = 1/(600 + R3)
600 + R3 = 1000
R3 = 400 ohm

a) Current at point d = I = 5 mA
b) V between d and b = 5 - 3 = 2 V
c) Req = R1 + R3 = 1000 ohm
d) When the switch is closed, Req = 600 + 400R3/(400 + R3)
I = 5/[600 + 400R3/400 + R3)]
so, the R3, R2 equivalent is less than R3 alone, Hence, Req decreases, I increases.