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The time constant of C-R circuit is...

The time constant of C-R circuit is

A

`(1)/(CR)`

B

`(C)/(R)`

C

`CR`

D

`(R)/(C)`

Text Solution

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The correct Answer is:
To find the time constant of a C-R (Capacitor-Resistor) circuit, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Components**: In a C-R circuit, we have a capacitor (C) and a resistor (R) connected in series. The behavior of the circuit is characterized by how the capacitor charges and discharges through the resistor. 2. **Definition of Time Constant**: The time constant (τ) of a C-R circuit is defined as the product of the resistance (R) and the capacitance (C). Mathematically, this is expressed as: \[ \tau = R \times C \] 3. **Units of Time Constant**: The time constant τ has the same units as time. Since resistance (R) is measured in ohms (Ω) and capacitance (C) is measured in farads (F), the unit of τ will be seconds (s). 4. **Current and Charge Equations**: The equations governing the current (I) and charge (Q) in the circuit can be expressed as: - For current: \[ I = I_0 e^{-\frac{t}{RC}} \] - For charge: \[ Q = Q_0 (1 - e^{-\frac{t}{RC}}) \] Here, \(I_0\) and \(Q_0\) are the initial current and charge, respectively. 5. **Conclusion**: The time constant τ, which is equal to R multiplied by C, is a crucial parameter in determining how quickly the capacitor charges or discharges in the circuit. ### Final Answer: The time constant of a C-R circuit is given by: \[ \tau = R \times C \]
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