4. Given the following sets of resistors and capacitors, rank the time it would

Question

4. Given the following sets of resistors and capacitors, rank the time it would take for them to charge (i.e. rank their time constants t) if connected to a battery (the circles are the terminals) All of the resistors are identical, and all of the capacitors are identical. [Hint: how do capacitors add in series & parallel compared to resistors] Longest Time - Shortest Time 5. Network A is charged to 12 Volts across the capacitor, A wire is then connected between its two terminals and so its capacitor begins to discharge. After 0.1 seconds, the capacitor has 4 V across it. What is the voltage across the capacitor 0.3 seconds after it begins to discharge? 6. You connect network B above to a battery of voltage V. If the two capacitors weren't identical ie, didn't have the same C),would they have the same voltage drop across them? Would they have the same charge on their plates? Justify your answer.

Explanation / Answer

Q4.

let resistance be R and each capacitor be C.

circuit A:

time constant=R*C

circuit B:

C and C are in parallel.

net capacitance=C+C=2*C

time constant=2*C*R

circuit C:

C and C are in series.

net capacitance=C*C/(C+C)=C/2

time constant=R*C/2

circuit D:

R and R in series.

net resistance=R+R=2*R

time constant=2*R*C

so ranking:

circuit B = circuit D > circuit A > circuit C

Q5.

discharging equation:

Voltage at any time t=12*exp(-t/T)

where T=time constant

at t=0.1 seconds, voltage=4 volts

==>4=12*exp(-0.1/T)

==>1/3=exp(-0.1/T)

==>T=0.091024 seconds

voltage at t=0.3 seconds

12*exp(-0.3/T)

=0.444 volts

Q6.

as they are connected in parallel, they will have same voltage across them

as charge=voltage*capacitance

the capacitor having higher capacitance will have higher charge.

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