Answer to Question #110948 in Electric Circuits for James

Question

Calculate (a) the value of the resistor Rx, such that the total power dissipated in the circuit is 2.5KW, and (b) the current flowing in each of the four resistors . R1=15ohms, R2=10ohms, R3=38ohms and R4=Rx.

Answer 1

As per the given question,

Here value of V and the diagram was not given, so I assumed that the given diagram is like given below,

$R_1=15\Omega, R_2=10\Omega, R_3=38\Omega R_4=R_x.$

a) P=VI

$I=\dfrac{2.5\times 1000}{250}=10A$

ii) $250=10(\dfrac{15\times 10}{15+10})+10\times\dfrac{38\times R_x}{38+R_x}$

$\Rightarrow 25=\dfrac{150}{25}+\dfrac{38R_x}{38+R_x}$

$\Rightarrow 25=6+\dfrac{38R_x}{38+R_x}$

$\dfrac{38R_x}{38+R_x}=19$

$\Rightarrow 38R_x=38\times 19+R_x\times 19$

$\Rightarrow 19R_x=38\times 19$

$\Rightarrow R_x=38\Omega$