A total resistance of 3.0 $\Omega$ is to be produced by combining an unknown resistor R with a 12 $\Omega$ resistor.What is the value of R and how is it to be connected to the 12 $\Omega$ resistor?
A)2.4$\Omega$, parallel
B)2.4 $\Omega$, series
C)4.0 $\Omega$, parallel
D)4.0 $\Omega$, series
E)9.0 $\Omega$, series

Question

Quizplus · Accepted Answer

To find the unknown resistor R, we can use the formula for calculating total resistance in a parallel circuit:

1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ...

We know that R2 (the 12 ohm resistor) has a resistance of 12 ohms, and we want the total resistance to be 3 ohms. Therefore:

1/3 = 1/R + 1/12

Solving for R, we get R = 4 ohms.

Since the total resistance is to be produced by combining R with the 12 ohm resistor, they must be connected in parallel. In a parallel circuit, the voltage across each resistor is the same, but the current is divided among the resistors. This means that the total current drawn from the power source will be greater than if only one resistor was used, but the overall resistance will be less.

A Total Resistance of 3 Ω\OmegaΩ Is to Be Produced by Combining an Unknown Resistor R

A Total Resistance of 3 $\Omega$ Is to Be Produced by Combining an Unknown Resistor R