Answer to Question #171508 in Electric Circuits for Paul

Question

Two resistor R and X connected parallel.The ammeter reads a current of 3A,when R is 5ohms, and 6A when R 2A.Determine the value of X

Answer 1

Explanations & Calculations

• As the question describes, the setup should be like the attached sketch.

• The ammeter reads the total current as it says & that is "the voltage applied to the resistor combination/the total resistance".
• Then by writing equations to the total current, this sum could be solved

$\qquad\qquad \begin{aligned} \small i_{total}&=\small i_x+i_R\\ \small 3A&=\small \frac{E}{X}+\frac{E}{5\Omega}\\ &=\small E\Big(\frac{1}{X}+\frac{1}{5}\Big)\cdots(1) \end{aligned}$ For the first combination of resistors

$\qquad\qquad \begin{aligned} \small 6A&=\small \frac{E}{X}+\frac{E}{2\Omega}\\ &=\small E\Big(\frac{1}{X}+\frac{1}{2}\Big)\cdots(2) \end{aligned}$ For the second arrangement

• By (1)/(2),

$\qquad\qquad \begin{aligned} \small \frac{1}{2}&=\small \frac{\large{\frac{1}{X}+\frac{1}{5}}}{\large{\frac{1}{X}+\frac{1}{2}}}\\ \small \frac{1}{X}&=\small \frac{1}{10}\\ \small X &=\small \bold{10\Omega} \end{aligned}$