What is the equivalent resistance between points a and b when R = 30 Ω?
A)27 Ω
B)21 Ω
C)24 Ω
D)18 Ω
E)7.5 Ω

Question

What is the equivalent resistance between points a and b when R = 30 Ω? 
A)27 Ω 
B)21 Ω 
C)24 Ω 
D)18 Ω 
E)7.5 Ω

Quizplus · Accepted Answer

The circuit can be simplified by combining the 15 Ω and 10 Ω resistors in series to get a total resistance of 25 Ω. Then, adding the 5 Ω resistor in parallel with the 25 Ω resistor results in an equivalent resistance of:

1/Requiv = 1/25 + 1/5
1/Requiv = 0.04
Requiv = 25 Ω

Finally, adding the 30 Ω resistor in series with the equivalent resistance gives a total resistance of:

Rtotal = 25 + 30
Rtotal = 55 Ω

Therefore, the equivalent resistance between points a and b is 55 Ω. However, the question asks for the equivalent resistance when R = 30 Ω. To find this, we can use a voltage divider equation:

Vab = 30 / (30 + 55) * 10V
Vab = 3V

Then, using Ohm's Law:

I = V / R
I = 3V / 30 Ω
I = 0.1A

Finally, using Ohm's Law again:

V = IR
V = 0.1A * 30 Ω
V = 3V

Since the voltage across the 30 Ω resistor and the voltage between points a and b are the same, the current passing through the 30 Ω resistor is the same as the current passing between points a and b. Therefore, the equivalent resistance between points a and b when R = 30 Ω is:

R = V / I
R = 3V / 0.1A
R = 30 Ω

Thus, the best choice is D.

What Is the Equivalent Resistance Between Points a and B