Which equation expresses the reciprocal of the total impedance for two parallel impedances as the sum of reciprocals?

• A. Z_total = Z1 + Z2
• B. 1/Z_total = 1/Z1 + 1/Z2
• C. Z_total = Z1 Z2 / (Z1+Z2)
• D. Z_total = Z1 - Z2

Answer: (B)

In parallel, the two impedances share the same voltage and the currents add. Using I = V/Z for each branch, the total current is I_total = V/Z1 + V/Z2. Since the total current also equals I_total = V/Z_total, you can divide both sides by V to get 1/Z_total = 1/Z1 + 1/Z2. This shows that the reciprocal of the total impedance is the sum of the reciprocals of the individual impedances.

If you solve this for Z_total, you’d get Z_total = Z1 Z2 / (Z1 + Z2), which is the actual parallel-impedance formula. The reciprocal form 1/Z_total = 1/Z1 + 1/Z2 is simply that same relationship written in reciprocal terms, which is exactly what the question asks for.

The other forms don’t match the asked expression: Z_total = Z1 + Z2 is the series case, and Z_total = Z1 - Z2 isn’t a valid combination for impedances.