Question

Find the charge q(t) on the capacitor and the current i(t) in the given LRC-series circuit. L =5/2 h, R = 10Ohm, C=1/20 f, E(t) = 200V,q(0) = 0 C, i(0) = 0 A

q(t) = _______C
i(t)=_____A
Find the maximum charge on the capacitor. (Round your answer to three decimal places.)
______C

Answer 1

To find the charge q(t) on the capacitor and the current i(t) in the given LRC-series circuit, we can use the equations q(t) = q(0) * e^(-t/RC) + [E(t)/R] * (1 - e^(-t/RC)) and i(t) = (E(t)/R) * e^(-t/RC). We can substitute the given values into these equations to find the charge and current. The maximum charge on the capacitor can be found by finding the value of q(t) as t approaches infinity using a limit.

Step-by-step explanation:

In an LRC-series circuit, we can find the charge on the capacitor and the current in the circuit by using the equations:

q(t) = q(0) * e^(-t/RC) + [E(t)/R] * (1 - e^(-t/RC))

i(t) = (E(t)/R) * e^(-t/RC)

Using the given values, we can substitute them into the equations to find the charge and current:

q(t) = 0 * e^(-t/(10*(1/20))) + [200/10] * (1 - e^(-t/(10*(1/20))))

i(t) = (200/10) * e^(-t/(10*(1/20)))

To find the maximum charge on the capacitor, we need to find the value of q(t) as t approaches infinity. This can be found using the limit:

lim(t->∞) q(t) = 0 * e^(-∞/(10*(1/20))) + [200/10] * (1 - e^(-∞/(10*(1/20))))

This limit is equal to the maximum charge on the capacitor. To find this value, we can simplify the limit and evaluate it, rounding to three decimal places.