The time constant for a series RC circuit in which the resistance is 100,000 ohms and the capacitance is 10uf is
A. 1,000,000 sec.
B. 10,000 sec.
C. 10 sec.
D. 1 sec.
The correct answer and explanation is:
The correct answer is C. 10 sec.
Explanation:
The time constant (τ) for a series RC (resistor-capacitor) circuit is calculated by multiplying the resistance (R) by the capacitance (C). The formula is:
τ=R×C\tau = R \times C
where
- RR is the resistance in ohms (Ω)
- CC is the capacitance in farads (F)
- τ\tau is the time constant in seconds (s)
Given the values:
- R=100,000 ΩR = 100,000 \, \Omega (100 kilo-ohms)
- C=10 μF=10×10−6 F=0.00001 FC = 10 \, \mu F = 10 \times 10^{-6} \, F = 0.00001 \, F
Calculate the time constant: τ=100,000×0.00001=1\tau = 100,000 \times 0.00001 = 1
This equals 1 second, which matches option D. However, notice the calculation needs to be double-checked carefully.
Recalculating: τ=100,000 Ω×10×10−6 F=100,000×0.00001=1 second\tau = 100,000 \, \Omega \times 10 \times 10^{-6} \, F = 100,000 \times 0.00001 = 1 \, \text{second}
So the time constant is actually 1 second, corresponding to option D.
Final check:
- 100,000 ohms = 105 Ω10^5 \, \Omega
- 10 microfarads = 10×10−6=10−5 F10 \times 10^{-6} = 10^{-5} \, F
Multiply:
105×10−5=105−5=100=1 second10^5 \times 10^{-5} = 10^{5 – 5} = 10^0 = 1 \, \text{second}
Therefore, the time constant is 1 second.
Summary: The time constant of a series RC circuit is the product of resistance and capacitance. When resistance is 100,000 ohms and capacitance is 10 microfarads, the time constant equals 1 second. This time constant describes how quickly the capacitor charges or discharges through the resistor. After one time constant, the voltage across the capacitor reaches approximately 63% of its final value. This property is important in timing circuits, filters, and signal processing applications. The 1-second time constant indicates a moderate speed of charging or discharging in this circuit.