For two impedances Z1 and Z2, what are the series and parallel formulas for total impedance?

For two impedances Z1 and Z2, what are the series and parallel formulas for total impedance?

• A. Series: Z1 Z2; Parallel: 1/(Z1 Z2)
• B. Series: Z1 + Z2; Parallel: 1/Z1 + 1/Z2
• C. Series: Z1 - Z2; Parallel: Z1 Z2
• D. Series: Z1 + Z2; Parallel: Z1 Z2 / (Z1 + Z2)

Answer: (B)

Impedances combine differently depending on how they’re connected. In series, impedances simply add: the total Z is Z1 plus Z2. In parallel, the currents add, so the total impedance comes from the reciprocal sum: 1/Z_total = 1/Z1 + 1/Z2. That can be written as Z_total = 1/(1/Z1 + 1/Z2) or, equivalently, Z_total = (Z1 Z2)/(Z1 + Z2). So the correct form uses series as Z1 + Z2 and parallel as Z1 Z2 divided by (Z1 + Z2). A form that writes the parallel result as 1/Z1 + 1/Z2 would be giving the total admittance, not the impedance.

Impedances combine differently depending on how they’re connected. In series, impedances simply add: the total Z is Z1 plus Z2. In parallel, the currents add, so the total impedance comes from the reciprocal sum: 1/Z_total = 1/Z1 + 1/Z2. That can be written as Z_total = 1/(1/Z1 + 1/Z2) or, equivalently, Z_total = (Z1 Z2)/(Z1 + Z2).

So the correct form uses series as Z1 + Z2 and parallel as Z1 Z2 divided by (Z1 + Z2). A form that writes the parallel result as 1/Z1 + 1/Z2 would be giving the total admittance, not the impedance.