# When Does Voltage Across Resistor Equal Voltage Across Inductor in RL Circuit?

• Engineering
• JordanU94
In summary, the conversation discusses a homework question about calculating the time at which the voltage across a resistor equals the voltage across an inductor in a series circuit with a step input of 100V. The person is unsure which equation to use, but knows that τ=L/R is relevant. They have been searching for a week and have found equations for finding current and time constants, but not the specific equation they need. Someone suggests looking up "LR series 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

JordanU94 said:

## 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

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

JordanU94 said:
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?

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.

## 1. What is the formula for calculating when voltage across resistor equals voltage across inductor in an RL circuit?

The formula for calculating this is VR = VL = IZ, where VR represents the voltage across the resistor, VL represents the voltage across the inductor, and IZ represents the total impedance of the circuit.

## 2. How do you determine the voltage across an inductor in an RL circuit?

The voltage across an inductor can be determined by using the formula VL = L(di/dt), where L is the inductance of the inductor and di/dt is the rate of change of current.

## 3. What is the significance of the voltage across resistor equaling the voltage across inductor in an RL circuit?

This signifies that the voltage drop across the inductor and resistor is equal, indicating that the circuit is in a steady state. This also means that the current in the circuit is constant.

## 4. What factors can affect the voltage across an inductor in an RL circuit?

The voltage across an inductor can be affected by the inductance of the inductor, the rate of change of current, and the resistance in the circuit. Additionally, the frequency of the AC power supply can also affect the voltage across the inductor.

## 5. How can I calculate the impedance of an RL circuit?

The impedance of an RL circuit can be calculated using the formula Z = √(R2 + (ωL)2), where R is the resistance in the circuit, ω is the angular frequency of the AC power supply, and L is the inductance of the inductor. This can also be calculated by using the individual values for resistance and reactance (ωL) and using Ohm's Law to find the total impedance.

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