Calculating when voltage across resistor = voltage across inductor in an RL circuit

[JordanU94]

Homework Statement

A step input of 100V is applied to a resistor of 50Ω in series with an inductor of 10H at time t=0. Calculate the time at which the voltage across the resistor equals the voltage across the inductor

Homework Equations

Im not sure which equation to use, i know τ=L/R is used, but that's all I am certain of

The Attempt at a Solution

I have no valid attempts :grumpy:

 

[gneill]

Homework Statement

A step input of 100V is applied to a resistor of 50Ω in series with an inductor of 10H at time t=0. Calculate the time at which the voltage across the resistor equals the voltage across the inductor

Homework Equations

Im not sure which equation to use, i know τ=L/R is used, but that's all I am certain of

The Attempt at a Solution

I have no valid attempts :grumpy:

Google is your friend. Look up "LR series circuit".

 

[JordanU94]

I have been for the past week, I've found equations to find the current in the circuit, and the time constants of the exponensial curve, but not what I'm looking for

 

[gneill]

I have been for the past week, I've found equations to find the current in the circuit, and the time constants of the exponensial curve, but not what I'm looking for

Well, what equations have you found?

 

[rezeew]

I would approach this problem by first understanding the basic principles of an RL circuit. In this case, we have a series circuit consisting of a resistor and an inductor, with a step input of 100V applied at time t=0.

The equation τ=L/R is used to calculate the time constant of the circuit, which represents the time it takes for the current in the circuit to reach 63.2% of its maximum value. In this case, the time constant is equal to the inductance (L) divided by the resistance (R).

To calculate the time at which the voltage across the resistor equals the voltage across the inductor, we can use the equation V_R = V_L = V_0 * (1 - e^(-t/τ)), where V_R is the voltage across the resistor, V_L is the voltage across the inductor, V_0 is the step input voltage, and t is the time.

Substituting the values given in the problem, we get 50 = 100 * (1 - e^(-t/τ)). Solving for t, we get t = 0.693 * τ = 0.693 * (10H/50Ω) = 0.1386 seconds.

Therefore, the voltage across the resistor will equal the voltage across the inductor at 0.1386 seconds after the step input is applied.