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

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Quizplus · Accepted Answer

Since the two resistors are identical, the voltage across each of them is equal. Let's call this voltage V1. The voltage across the variable resistor (R_x) is then V-V1. The total resistance of the circuit can be calculated using the formula: $R_{tot} = R + R_{parallel}$ where R is the resistance of one of the identical resistors, and $R_{parallel}$ is the total resistance of the two resistors in parallel. We can calculate $R_{parallel}$ using the formula: $\frac{1}{R_{parallel}} = \frac{1}{R} + \frac{1}{R}$ Simplifying this, we get: $R_{parallel} = \frac{R}{2}$ So the total resistance becomes: $R_{tot} = R + \frac{R}{2} = \frac{3R}{2}$ The current in the circuit can be calculated using Ohm's Law: $I = \frac{V}{R_{tot}}$ The current through each of the identical resistors is then: $I_1 = \frac{V_1}{R} = \frac{V}{2R_{tot}}$ The voltage across the variable resistor can now be calculated using Ohm's Law again: $V-V_1 = I_1R_x$ Substituting the expressions for $I_1$ and $R_{tot}$, we get: $V-V_1 = \frac{VR_x}{3R}$ We know that $V_1 = 11eab929_294a_3cb9_99e6_81f4fcb9fe96_TB4470_00$. Substituting this, and simplifying, we get: $V-V_1 = \frac{8V}{9}$ So the variable resistor needs to have a resistance of: $R_x = \frac{8V}{9} imes \frac{R}{V} = \frac{8R}{9} = 8 \Omega$ Therefore, the answer is C) 8.0 Ω.

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