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  • An electrical circuit consists of three resistors R1, R2, and R3 connected in a combination of series and parallel. The circuit is powered by a constant voltage sou

An electrical circuit consists of three resistors R1, R2, and R3 connected in a combination of series and parallel. The circuit is powered by a constant voltage source of 48V. The currents flowing through each resistor are measured and recorded:

Resistor Current (A)
R1 2.0
R2 1.5
R3 3.0

Using this data, calculate the equivalent resistance of the entire circuit is:

Option: 1

8.5 \Omega


Option: 2

79.5 \Omega


Option: 3

59.5 \Omega


Option: 4

3.0 \Omega


Answers (1)

best_answer

In a circuit with a combination of series and parallel resistors, you need to first determine the equivalent resistance of the individual series and parallel segments before calculating the overall equivalent resistance.

For the parallel segment (Rp), the reciprocal of the total resistance (1/Rp, eq) is the sum of the reciprocals of the individual resistances:

                    \frac{1}{R_{p, eq}} = \frac{1}{R_{2}} + \frac{1}{R_{3}}

Now, calculate Rp, eq:

        R_{p, eq} = \frac{1}{\frac{1}{R_{2}} + \frac{1}{R_{3}}} = \frac{1}{\frac{1}{1.5} + \frac{1}{3}} = 1.0 \Omega

Now, the total equivalent resistance (Req) is the sum of the series resistance (R1) and the parallel equivalent resistance (Rp, eq):

                    R_{eq} = R_{1} + R_{p,eq} = 2.0 + 1.0 = 3.0 \Omega

Hence, the equivalent resistance of the entire circuit is 3.0 \Omega.

 

 

Posted by

avinash.dongre

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