If a simple AC voltage divider has Z1 equal to Z2, what fraction of the source voltage Vs appears across Z2?

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Multiple Choice

If a simple AC voltage divider has Z1 equal to Z2, what fraction of the source voltage Vs appears across Z2?

Explanation:
In a simple AC voltage divider, the voltage across the second element is Vs times the impedance of that element divided by the total impedance: V2 = Vs · Z2 / (Z1 + Z2). Since the two impedances are in series, the same current flows through both, so the voltage drops are proportional to their impedances. If Z1 and Z2 are equal, Z2/(Z1 + Z2) becomes Z/(Z + Z) = Z/(2Z) = 1/2. Therefore, the voltage across the second element is half of the source: V2 = Vs/2. This holds whether the impedances are purely resistive or complex, because the Z cancels out when they are equal, leaving a clean 1/2 division.

In a simple AC voltage divider, the voltage across the second element is Vs times the impedance of that element divided by the total impedance: V2 = Vs · Z2 / (Z1 + Z2). Since the two impedances are in series, the same current flows through both, so the voltage drops are proportional to their impedances.

If Z1 and Z2 are equal, Z2/(Z1 + Z2) becomes Z/(Z + Z) = Z/(2Z) = 1/2. Therefore, the voltage across the second element is half of the source: V2 = Vs/2. This holds whether the impedances are purely resistive or complex, because the Z cancels out when they are equal, leaving a clean 1/2 division.

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