How to Find Equivalent Time Constant of RC Circuit
Consider a circuit given below
In this circuit, you have to find the current and charge at a time ?.
It would be difficult to find the charge using KVL.
There is another way to find the charge in the capacitor.
Let’s assume the equivalent circuit as shown in the figure.
Step 1. Find equivalent time constant
Step 2. Charge on the capacitor at any time ? is
?=?_0 (1−?^(−?/?_? ) )
Using Kirchhoff’s laws, we can find current in others part of the circuit also.
Q. In the given circuit, the switch S is closed at time ?=0. The charge on the capacitor at any instant ? is given by
?=?_0 (1−?^(−??) ). Find the value of ?_0 ??? ? in terms of given parameters as shown in the figure.
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Problem 5.6 |Magnetostatics |Griffith |3rd ed.
Problem 5.6
(a) A phonograph record carries a uniform density of "static electricity" ?. If it rotates at angular velocity ?, what is the surface current density ? at a distance ? from the center?
(b) A uniformly charged solid sphere, of radius ? and total charge ?, is centered at the origin and spinning at a constant angular velocity ? about the ? axis. Find the current density ? at any point (?, ?,?) within the sphere.
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