Two identical resistors of resistance R = 24 Ω and a variable resistor R_x are connected to an ideal battery of voltage V as shown in the figure. What should be the value of the variable resistance R_x 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

Quizplus · Accepted Answer

Since the two resistors are identical, the voltage across each of them is equal. Let's call that voltage V1. Similarly, let's call the voltage across the variable resistor V2. Using the voltage divider rule, we can write: V1 = V * R / (2R + R_x) V2 = V * R_x / (2R + R_x) Since we want V1 = 11eab6cc_1d76_cda2_a957_872c82916e1a_TB4469_11, we can set up the following equation: 11eab6cc_1d76_cda2_a957_872c82916e1a_TB4469_11 = V * R / (2R + R_x) Solving for R_x gives: R_x = (V * R / 11eab6cc_1d76_cda2_a957_872c82916e1a_TB4469_11) - 2R Substituting the given values, we get: R_x = (V * 24 Ω / 11eab6cc_1d76_cda2_a957_872c82916e1a_TB4469_11) - 2 * 24 Ω R_x ≈ 8.0 Ω Therefore, the value of the variable resistor should be approximately 8.0 Ω, which is answer choice C.

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