Experiment 5 RC Circuits and Time ConstantsPhysics Laboratory 202/212 a. at the

Question

Experiment 5 RC Circuits and Time ConstantsPhysics Laboratory 202/212 a. at the beginning of the process b. near the middle of the process c. at the end of the process d. after one time constant 2. When a capacitor discharges through a resistor, the current in the ciroult is minimum a. atthe beginning ofthe process b. near the middle of the process c at the end of the process d. after one time constant 3. Another way to desobe the discharge tme of an RC arut is to use a interval called the half-ife, which is defined as the time for the capacitor to lose half its initial charge. Is the time constant longer or shorter than the hiile? Explain your reasoning 4. Does charging a capoor in an RCorcutto29% its mamum vale take lorger or shorter than one time constant? Explain. 5. A capacitor and a resistor are connected through a switch to an emf. At the instant just after the switch is closed a the current in the circuilt is zero. b. the voltage across the capacitor is the same as the emf c the voltage across the resistor is zero d. the voltage across the resistor is the same as the emt e Both a and c are true

Explanation / Answer

1) a) at the biginig of the process.
Initially the potential difference across the resistor is maximum. so, current through the resistor is maximum.

2) c) at the end of the process.
After a long time, the potential difference across the capacitor is zero. so, potential difference across resistor also become szero. so, current through the resistor becomes zero.

3)

at time t = t1/2

VC = Vmax*e^(-t/T)

Vmax/2 = Vmax*e^(-t/T)

(1/2) = e^(-t/T)

ln(1/2) = -t/T

==> T = -t/ln(1/2)

T = 1.44*t/12

so, time constant = 1.44 times of half-life

time constant is noger than half-life

4)

at time t,

VC = Vmax*(1 - e^(-t/T))

0.25*Vmax = Vmax*(1 - e^(-t/T))

0.25 = 1 - e^(-t/T)

e^(-t/T) = 1 - 0.25

-t/T = ln(0.75)

t = -T(ln(0.75)

= 0.288*T

time taken is shorter than time constant

5) d) the voltage across the resistor is same as emf

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