NEIEP Mechanics Practice Exam

If two capacitors in parallel have equal reactance of 40 ohms, what is the total reactance?

1. 10 ohms

2. 20 ohms

3. 30 ohms

4. 40 ohms

The correct answer is: 20 ohms

In a parallel arrangement, the total reactance of capacitors is calculated using the formula for combining reactances, which is analogous to combining resistances in parallel. For two capacitors with equal reactance, the formula simplifies as follows: The total reactance \( X_t \) can be determined using the reciprocal formula: \[ \frac{1}{X_t} = \frac{1}{X_1} + \frac{1}{X_2} \] Given that both capacitors have a reactance of 40 ohms, this means: \[ \frac{1}{X_t} = \frac{1}{40} + \frac{1}{40} \] This can be simplified to: \[ \frac{1}{X_t} = \frac{2}{40} = \frac{1}{20} \] Now, if we take the reciprocal of both sides, we find: \[ X_t = 20 \text{ ohms} \] This demonstrates that the total reactance of the two capacitors in parallel, each having a reactance of 40 ohms, indeed sums up to 20 ohms. This calculation process highlights how reactance behaves in parallel