In the circuit shown in the figure, switch S can be closed on either point A or
ID: 2255626 • Letter: I
Question
In the circuit shown in the figure, switch S can be closed on either point A or C, but not both at the same time. a) What is the equivalent resistance between points A and B?
b) Determine the current through R1 when the switch S is closed on A. c) At what rate is energy dissipated by R1 when the switch S is closed on A? d) Determine the current through R4 when the switch S is closed on C. Use the following quantities:
V1 = V2 = 12 V
R1 = R4 = 1.0 ?
R2 = R3 = 2.0 ?
In the circuit shown in the figure, switch S can be closed on either point A or C, but not both at the same time. a) What is the equivalent resistance between points A and B? Determine the current through R1 when the switch S is closed on A. c) At what rate is energy dissipated by R1 when the switch S is closed on A? d) Determine the current through R4 when the switch S is closed on C. Use the following quantities:Explanation / Answer
Case 1: Switch closed on A.
a). Equivalent resistance between A and B is R1 + R2*R3/(R2+R3) since R2 and R3 are in parallel which in turn is in series with R1.
b). Let R = R1 + R2*R3/(R2+R3)
= R = 1 + 2*2/2+2
= 1 + 1
= 2 ohm
V2/R = current through the circuit = current through R1 as it is in series.
V2/R = 12/2 = 6 ampere.
Current through R1 = 6 A
c). Rate of dissipation across R1 = Energy per unit time = I^2*R1
= 6^2 * 1
=36 J per second
d) Current through R4 for switch at C
let current through R4 be i.
-V2 -i*R4 + V1 = 0
-12 - i*R4 +12 = 0.
hence i=0.
This implies the current through the circuit is 0 in this case as V1 = V2 = 12 and since both are connected not in series, ie, the same magnitude and opposite potentials cancel each other, hence the current is 0.