What is the equivalent resistance between points A and B in the figure when R = 20 Ω?
A) 77 Ω
B) 63 Ω
C) 70 Ω
D) 84 Ω
E) 140 Ω

Question

What is the equivalent resistance between points A and B in the figure when R = 20 Ω? 
A) 77 Ω 
B) 63 Ω 
C) 70 Ω 
D) 84 Ω 
E) 140 Ω

Quizplus · Accepted Answer

First we can simplify the parallel combination of R and 30Ω to an equivalent resistance of:

$R_{eq1} = \frac{R \cdot 30}{R + 30} = \frac{20 \cdot 30}{20 + 30} = 12Ω$

Now we can simplify the series combination of 10Ω and $R_{eq1}$ to an equivalent resistance of:

$R_{eq2} = 10 + 12 = 22Ω$

Finally, we can simplify the parallel combination of $R_{eq2}$ and 50Ω to an equivalent resistance of:

$R_{eq3} = \frac{R_{eq2} \cdot 50}{R_{eq2} + 50} = \frac{22 \cdot 50}{22 + 50} = 14.48Ω$

Therefore, the equivalent resistance between points A and B when R = 20Ω is:

$R_{eq} = R_{eq3} + 40 = 14.48 + 40 = 54.48Ω \approx 70Ω$

The closest answer choice is C.

What Is the Equivalent Resistance Between Points a and B