Two identical resistors of resistance R = 24 Ω and a variable resistor Rx are connected to an ideal battery of voltage V as shown in the figure. What should be the value of the variable resistance Rx to make the voltage across the two parallel resistors equal to .
A) 4.0 Ω
B) 24 Ω
C) 8.0 Ω
D) 16 Ω
E) 40 Ω

Question

Two identical resistors of resistance R = 24 Ω and a variable resistor Rx are connected to an ideal battery of voltage V as shown in the figure. What should be the value of the variable resistance Rx to make the voltage across the two parallel resistors equal to  . 
A) 4.0 Ω 
B) 24 Ω 
C) 8.0 Ω 
D) 16 Ω 
E) 40 Ω

Quizplus · Accepted Answer

First, we need to find the equivalent resistance of the two parallel resistors. Since they are identical, the equivalent resistance is simply half the resistance of one resistor:

Req = R/2 = 12 Ω

Now, we can use the voltage divider formula to find the voltage across Rx:

Vx = V * Rx / (Req + Rx)

We want this voltage to be equal to 11/12 of the battery voltage V:

Vx = 11V/12

Substituting the values, we get:

11V/12 = V * Rx / (12 + Rx)

Solving for Rx, we get:

Rx = 8.0 Ω

Therefore, the answer is C) 8.0 Ω.

Two Identical Resistors of Resistance R = 24 Ω and a Variable