The resistance of each resistor

The total resistance of the circuit is 10 Ω. If the resistors R1 and R3 are swapped then the total resistance of the circuit will increase 100 times. If the resistors R2 and R3 are swapped then the total resistance of the circuit will increase by 0.2%.

3Resistors

Find the resistance of each resistor.

Solution.

There are three different circuits.

The total resistance of the first or original circuit is given by the formula

R1*R2/(R1 + R2) + R3 = 10

The total resistance of the second circuit is given by the formula

R2*R3/(R2 + R3) + R1 = 1000

The total resistance of the third circuit is given by the formula

R1*R3/(R1 + R3) + R2 = 10.02

Solving the system of three equations, we obtain

R1 ≈ 997.59 Ω
R2 ≈ 6.02 Ω
R3 ≈ 4.02 Ω

 
 

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