First, we need to find the time constant of the LR circuit. The time constant (τ) is given by the formula: τ = L / R where L is the inductance (34 H) and R is the resistance of the resistor
The Correct Answer and Explanation is:
Sure! To find the time constant τ\tau of an LR circuit, you use the formula: τ=LR\tau = \frac{L}{R}
where
- LL is the inductance (in henrys, H),
- RR is the resistance (in ohms, Ω\Omega).
Given:
- L=34 HL = 34 \, \text{H}
- R=R = (resistance value not provided, so let’s call it RR)
The time constant is then: τ=34Rseconds\tau = \frac{34}{R} \quad \text{seconds}
Explanation
The time constant τ\tau of an LR circuit is a measure of how quickly current builds up or decays in the circuit when the voltage is suddenly applied or removed. An LR circuit consists of an inductor LL and a resistor RR connected in series with a voltage source.
When voltage is applied, the current does not instantaneously reach its maximum value due to the inductor’s opposition to changes in current (inductive reactance). Instead, the current increases gradually. The time constant τ\tau defines the characteristic time it takes for the current to reach approximately 63.2% of its final steady-state value.
The time constant is determined by the ratio of the inductance to the resistance: τ=LR\tau = \frac{L}{R}.
- Inductance LL: This is the property of the coil or inductor that resists changes in current. A higher inductance means the circuit resists current change more strongly, so the time constant τ\tau increases.
- Resistance RR: This opposes the flow of current. A higher resistance causes the current to reach its final value faster because the voltage drop across the resistor is higher, so the time constant τ\tau decreases.
Physically, τ\tau represents the time it takes for energy stored in the magnetic field of the inductor to either build up or dissipate significantly. After a time equal to about 5τ5\tau, the current effectively reaches steady-state (practically 100%).
For example, if you know the resistance value RR, say R=10 ΩR = 10 \, \Omega, then the time constant would be: τ=34 H10 Ω=3.4 seconds\tau = \frac{34 \, \text{H}}{10 \, \Omega} = 3.4 \, \text{seconds}
This means it takes about 3.4 seconds for the current to reach 63.2% of its final value when the circuit is switched on.
In summary, the time constant τ\tau helps us understand how quickly an LR circuit responds to changes, which is crucial in designing circuits for timing, filtering, and transient analysis
.