A 1 000-V battery, a 3 000-Ω resistor, and a 0.50-μF capacitor are connected in series with a switch. The time constant for such a circuit, designated by the Greek letter, τ, is defined as the time that the capacitor takes to charge to 63% of its capacity after the switch is closed. What is the current in the circuit at a time interval of τ seconds after the switch has been closed?

The current in the circuit at a time interval of τ seconds after the switch has been closed is 0.123 A

Explanation:

The time constant for an R and C in series circuit is given by τ = RC.

R = 3000 ohms, C = 0.5 × 10⁻⁶ F = 5.0 × 10⁻⁷ F

τ = 3000 × 5 × 10⁻⁷ = 0.015 s

The voltage across a capacitor as it charges is given be

V(t) = Vs (1 - e⁻ᵏᵗ)

where k = 1/τ

At the point when t = τ, the expassion becomes

V(t = τ) = 1000 (1 - e⁻¹) = 0.632 × 1000 = 632 V

Current flows as a result of potential difference,.

Current in the circuit at this time t =  τ is given by

I = (Vs - Vc)/R

Vs = source voltage = 1000 V

Vc = Voltage across the capacitor = 632 V

R = 3000 ohms

I = (1000 - 632)/3000 = 0.123 A

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.