Answer to Question #166742 in Electric Circuits for Richard

Question

A resistance of 10 ohms is connected in series with two resistances each of 15 ohms arrange in parallel. What resistance must be shunted across this parallel combination so that the total current shall be 1.5 amps with 20 volts applied? Draw a diagram

Answer 1

$\frac{1}{Req} = \frac{1}{R2} + \frac{1}{R3} + \frac{1}{R4} = \frac{1}{Req} = \frac{1}{15} + \frac{1}{15} + \frac{1}{R1}$

$\frac{1}{Req} = \frac{2}{15} + \frac{1}{R}$

$Req = \frac{2R+15}{15R}$

R1 = 10 Ohms, Given

Therefore, Total Res. (Req) is given by:

$Req = R1 + \frac{15R}{2R+15} = 10 + \frac{15R}{2R+15}$

Given Current I = 1.5 A

And V = 20V

Therefore,

$Req = \frac({V}{I} = \frac{20}{1.5} = 13.33$

$Req = 13.33 = 10 + \frac{15R}{2R+15}$

On solving above, R = 5.98 Or 6 Ohms.

Final Answer R = 6 Ohms