Find the impedance of a circuit consisting of two series-connected resistors with resistances of 10 ohms and 40 ohms

| January 3, 2021 | education

Find the impedance of a circuit consisting of two series-connected resistors with resistances of 10 ohms and 40 ohms by how much the impedance will change if the resistors are connected in parallel.

R1 = 10 ohms.
R2 = 40 ohms.
Rpos -?
Rpar -?
ΔR -?
When the conductors are connected in series, the total resistance of the circuit Rpos will be the sum of the connected resistances R1 and R2: Rpos = R1 + R2.
Rpos = 10 Ohm + 40 Ohm = 50 Ohm.
When the conductors are connected in parallel, the total resistance of the circuit Rpairs is determined by the formula: 1 / Rpar = 1 / R1 + 1 / R2.
1 / Rpair = 1 / R1 + 1 / R2 = (R1 + R2) / R1 * R2.
Rpair = R1 * R2 / (R1 + R2).
Rpair = 10 Ohm * 40 Ohm / (10 Ohm + 40 Ohm) = 8 Ohm.
ΔR = Rposl – Rpair = 50 Ohm – 8 Ohm = 42 Ohm.
Answer: Rpos = 50 Ohm, Rpair = 8 Ohm, ΔR = 42 Ohm.



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