College Physics Problem Capacitor / Inductor

[aamartineng17]

A 10.0 Microfarad Capacitor is charged to 170 Micro Coulombs then connected across the ends of a 4.00mH inductor.

(a) Find the maximum current in the inductor.

(b) At the instant the current in the inductor is maximum. How much charge is on the capacitor parallel plates?

(c) Find the maximum potential across the capacitor.

(d) At the instant the potential across the capacitor is maximum. What is the current in the inductor?

(e) Find the maximum energy stored in the inductor.

(f) At the instance the energy stored in the inductor is maximum. what is the current in the circuit?

I am really stuck on calculating this physics problem, especially part a. Could someone please give me some assistance in calculating this Physics Problem. I really appreciate your help. Thanks

 

[gneill]

A 10.0 Microfarad Capacitor is charged to 170 Micro Coulombs then connected across the ends of a 4.00mH inductor.

(a) Find the maximum current in the inductor.

(b) At the instant the current in the inductor is maximum. How much charge is on the capacitor parallel plates?

(c) Find the maximum potential across the capacitor.

(d) At the instant the potential across the capacitor is maximum. What is the current in the inductor?

(e) Find the maximum energy stored in the inductor.

(f) At the instance the energy stored in the inductor is maximum. what is the current in the circuit?

I am really stuck on calculating this physics problem, especially part a. Could someone please give me some assistance in calculating this Physics Problem. I really appreciate your help. Thanks

Hi aamartineng17, Welcome to Physics Forums.

These kinds of problems are often easier if you think in terms of conservation laws. Here there are two energy storage devices (a Capacitor and an Inductor) which are going to trade energy back and forth. The result is oscillations of current and voltage.

When the circuit begins operation, only the capacitor has any energy stored since it has an initial voltage; There's no current flowing so the inductor has no stored energy.

What do you know about energy for these devices? Do you have formulas?

 

[aamartineng17]

Hello Everyone,

For the Following Physics Problem listed below:

I tried solving the problem, here were my results:

(Part a)

*Note: That the charged Capacitor is connected across an inductor.
The Equation for the voltage of a capacitor is the following: V = Q / C
For this problem Q = 1.7 x 10^-4 C, C = 1 x 10^-5 F
I calculated the Voltage of Capacitor to be:
V = Q / C = 1.7 x 10^-4 C / 1 x 10^-5 F = 17 Volts

I know that since the Capacitor is connected across the inductor I know that the inductor will then have a potential difference of 17 Volts.

**Note: At the instant when the charge on the capacitor reaches zero, Q = 0, the current in the Inductor has reached its max value, but at this instant the current in the Inductor is not changing, [-L (Delta I / Delta t) = Q / C = 0). At this moment, the magnetic field B in the inductor is also a maximum.

*** Note: I then calculated the Resonance Frequency using the following equation:
f = fo = (1 / 2* pie) * sqrt (1 / L * C)
f = fo = (1 / 2 * pie) * sqrt ( 1 / (4 x 10^-2 H) * (1.7 x 10^-4 C)
f = fo = 193 Hz

I then used the following equation
XL = 2 * pie*f* L = 4.851 ohms (the reactance for inductor)

I then used the Equation V = I * XL , to calculate the max current in inductor:

I = V / XL = 17 V / 4.851 ohms = 3.50 A (Calculated Max Current of Inductor)

I would really appreciate it if someone could please tell me if this is the correct way to solve (Part A) of this problem. Thanks Again for your time and help. I really appreciate and value your time and help!

 

[gneill]

When the charge reaches zero on the capacitor and the inductor has its maximum current, the voltage across the capacitor (and thus the inductor, too) will be zero. So your solution method for the current doesn't look right. (Also, it implies a steady-state AC situation, and you're looking for an instantaneous value in a transient situation).

Also, you appear to have plugged in the charge on the capacitor rather than the capacitance in your workings for the resonance frequency.

I might suggest that you look at it from an energy point of view. Capacitors store energy in electric fields, so their maximum energy stored corresponds to when they have a maximum potential difference across them. Inductors store energy in magnetic fields, and have maximal energy stored when their currents are maximum...

 

[asteriatic]

I am happy to assist you with this physics problem. Let's break down each part and use the relevant equations to find the answers.

(a) The maximum current in the inductor can be found using the equation I = V/R, where V is the voltage across the inductor and R is the resistance. In this case, the voltage is given by V = Q/C, where Q is the charge on the capacitor and C is the capacitance. Therefore, the maximum current in the inductor is I = Q/(RC). Plugging in the values given, we get:

I = (170 microCoulombs)/[(4.00mH)(10.0 microfarads)] = 4.25 A

(b) At the instant the current in the inductor is maximum, the charge on the capacitor will be equal to the maximum charge that the inductor can pass through, which is given by Q = CV. Using the values given, we get:

Q = (10.0 microfarads)(4.25 A) = 42.5 microCoulombs

(c) The maximum potential across the capacitor can be found using the equation V = Q/C, where Q is the charge on the capacitor and C is the capacitance. Plugging in the values given, we get:

V = (42.5 microCoulombs)/(10.0 microfarads) = 4.25 V

(d) At the instant the potential across the capacitor is maximum, the current in the inductor will be zero, as there is no change in the voltage across the inductor. Therefore, the current in the inductor is also zero.

(e) The maximum energy stored in the inductor can be found using the equation E = (1/2)LI^2, where L is the inductance and I is the current in the inductor. Plugging in the values given, we get:

E = (1/2)(4.00mH)(4.25 A)^2 = 36.0 microJoules

(f) At the instant the energy stored in the inductor is maximum, the current in the circuit will be zero, as there is no change in the energy stored in the inductor. Therefore, the current in the circuit is also zero.

I hope this helps you in solving this physics problem. Remember to always use the relevant equations and units when solving problems in