The figure below shows three sections of circuit that are to be connected in tur
ID: 1460314 • Letter: T
Question
The figure below shows three sections of circuit that are to be connected in turn to the same battery via a switch. The resistors am all identical, as are the capacitors. (a) When steady state has been reached (i.e. the capacitors are all fully charged), rank the sections according to the charge on the capacitor, largest first. (b) Given resistance R = 1 m ohm for each resistor and C = 1mu F, write down the time constant for each circuit. Rank the circuits according to the time taken for each capacitor to reach 50% of its maximum charge, starting with the shortest time. (c) If the battery voltage is 2V, what is the value of the current through the battery if you wait long enough for all the capacitors to he fully charged in each of the 3 cases?Explanation / Answer
in fig 1, R1 and R2 are in series, Rnet = R1+R2
in fig,2 , R1 and R2 are in parallel, 1/Rp = 1/R1 + 1/R2
Rp = R1R2/(R1+R2)
in fig 3, R1 and R2 are in series, R net = R1+ R2
also Charge Q = CV
since all have same capacitors, Cnet will be same in all figures
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b. Time constant T = Rc
in fig 1: Rnet = 1+1 = 2 m ohms
T = 2 e -3 * 1 e -6 = 2 ns
in fig 2, Rnet = 1*1/(1+1) = 0.5 mohms
T = 2e -3 * 0.5 e -6 = 1 ns
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Time constant T = Rc
in fig 3: Rnet = 1+1 = 2 m ohms
T = 2 e -3 * 1 e -6 = 2 ns
use the equation for Charge Q = Qo (1- e^ -t/RC)
for fig 1, 1-e^-t/Rc = 0.5
e^-t/RC = 0.5
-t/RC = ln 0.5 = 0.693
t = 0.693* 2 ns = 1.386 ns
in fig 2, t = 0.693 * 1 ns = 0.693 ns
in fig 3, t = 1.386 ns
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Current i = V/R
in fig1, I1 = 2/2 e -3 = 1000 A
in fig i2, = 2/1 e -3 = 2000 A
in fig 3, 2/2e -3 = 1000A