PLZ SHOW FULL WORK WITH NUMBERS ,, APPRECIATE IT Problem 3-old exam question: Th

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PLZ SHOW FULL WORK WITH NUMBERS ,, APPRECIATE IT

Problem 3-old exam question: The switch S in the figure at the right has been closed for a long time. A voltmeter is connected across the capacitor C 1.85 Enf x 102 F. The emf of the battery is 27 v and resistors 100 2, and R3 20 2 50 2, R2 (a) What is the voltmeter's reading when the switch has been closed for a long time? Show your work and reasoning for full credit. [Ans: 18 volts] (b) Assume the switch is now just open t 00. Then it is observed that voltage across the capacitor C is given in the figure at the right. Using the information given about the circuit and in the graph, E (1) show two different methods to a determine the time constant when the switch is open (If you use the graph to get the info, you need to clearly show how to do it on the graph. (2) Evaluate the two results comment on the discrepancy if due to the measurement uncertainty or due to your possible calculation mistake NAM R2 R3 Time (s)

Explanation / Answer

Capacitor when fully charged blocks DC current

hence when capacitor gets fully charged it will behave as open circuit

Volatge across it will be equal to that across R2

=>

voltage across R2:(100/150)*27=18V

b)

First part (from graph)

When volatge reaches 0.37 of its initial value that time gives us

the time constant

0.37*18=6.66V

Graph isn't very clear to me but it will be around 2.1sec

second Method:

Time constant of RC circuit is given by : CR

IT is a very standard result , derivation of which is also very simple:

Let i be current through Capacitor and q be charge on it :

volatge across Cap=q/C

q/C=I(R)

now I=dq/dt

this differential equation can be solved very easily

we get t/RC term in this RC is time constant

RC=(R2+R3)C=2.22sec

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