Question

A 2.00-µF and a 7.50-µF capacitor can be connected in series or parallel, as can a 25.0-kQ and a 100-ko resistor. Calculate the four RC time constants possible from connecting the resulting capacitance and resistance in series.

a) 2.00 × 25.0 × 103 µF
b) 7.50 × 25.0 × 103 µF
c) 2.00 × 100 × 103 µF
d) 7.50 x 100 x 103 µF

Answer 1

To calculate the four RC time constants for connecting capacitances and resistances in series, first determine the equivalent capacitance for series and parallel connections, and then the equivalent resistance for series and parallel connections. Use these equivalent values to calculate RC time constants for each possible configuration using the formula τ = RC.

Step-by-step explanation:

To find the four RC time constants possible from connecting the given capacitances and resistances in series, we first need to calculate the equivalent capacitance in both series and parallel combinations, and the equivalent resistance in both series and parallel combinations.

For capacitors in series, the formula is 1/Ceq = 1/C1 + 1/C2. For capacitors in parallel, the equivalent capacitance is Ceq = C1 + C2. For resistors, the formulas are reversed: in series, Req = R1 + R2, and in parallel, 1/Req = 1/R1 + 1/R2.

• Series Capacitance: 1/Ceq = 1/2.00 µF + 1/7.50 µF
• Parallel Capacitance: Ceq = 2.00 µF + 7.50 µF
• Series Resistance: Req = 25.0 kΩ + 100 kΩ
• Parallel Resistance: 1/Req = 1/25.0 kΩ + 1/100 kΩ

Once we have the equivalent capacitances and resistances, we can use the RC time constant formula, τ = RC. We calculate this for each combination of equivalent capacitance and resistance:

1. τ (Series C & Series R)
2. τ (Series C & Parallel R)
3. τ (Parallel C & Series R)
4. τ (Parallel C & Parallel R)

After performing the calculations, we get the four RC time constants.