# Calulating time constant

#### kevinh111

Joined Jan 19, 2012
2
Hey guys, have a question on a homework assignment related to RL time constants.

"A constant voltage is applied to a RL circuit at time t=0. The voltage across the inductance is 20 V at 3.46ms and 5 V at 25ms. Obtain R if L = 2H."

Given the equation T(tau/time const.) = L / R, how do I first calculate the time constant of the circuit in order to calculate the resistance?

#### t_n_k

Joined Mar 6, 2009
5,455
If the DC supply is Vd

Then

$$V_L(t)=V_de^{\frac{-t}{\tau}}$$

at t=3.46ms

$$V_L(3.46ms)=V_de^{\frac{-0.00346}{\tau}}=20$$

at t=25ms

$$V_L(25ms)=V_de^{\frac{-0.025}{\tau}}=5$$

Solve the two equations to find Tau

#### kevinh111

Joined Jan 19, 2012
2
Awesome, thanks for the quick response.

I am having some difficulties solving for Tau, the answer I obtained is that tau = 0.00465, using mathematica.

#### t_n_k

Joined Mar 6, 2009
5,455
The correct value for the time constant is 15.54ms.

Divide the two equations and take the natural logarithm of the result.