The total resistance of the circuit is 10 Ω. If the resistors R_{1} and R_{3} are swapped then the total resistance of the circuit will increase 100 times. If the resistors R_{2} and R_{3} are swapped then the total resistance of the circuit will increase by 0.2%.

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

R_{1}*R_{2}/(R_{1} + R_{2}) + R_{3} = 10

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

R_{2}*R_{3}/(R_{2} + R_{3}) + R_{1} = 1000

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

R_{1}*R_{3}/(R_{1} + R_{3}) + R_{2} = 10.02

Solving the system of three equations, we obtain

R_{1} ≈ 997.59 Ω

R_{2} ≈ 6.02 Ω

R_{3} ≈ 4.02 Ω