Answer to Question #302271 in Electric Circuits for Liam

Question

A 36-ohm resistor is connected in parallel with an unknown resistor R. Their combination is then connected in series with a 12-ohm resistor. Find the value of R such that power drawn by the parallel combination of 36 ohms and R is equal to the power in the 12-ohm resistor.

Answer 1

Explanations & Calculations

• Get the equivalent resistance of the parallel combination and then consider its power to be equal to that of the 12 Ohm resistor.
• The equivalent resistance is

$\qquad\qquad \begin{aligned} \small R_{eq}&=\small \frac{36R}{36+R}\\ \end{aligned}$

• Then since the power is equal to eachother's

$\qquad\qquad \begin{aligned} \small P= i^2R_{eq}&=\small i^2.12\\ \small R_{eq}&=\small 12\\ \small \frac{36R}{36+R}&=\small 12 \end{aligned}$

• When the equivalent is considered, the same current passes through each.
• You now can give it a try to get the answer.