PHY 7B Study Guide - Quiz Guide: Electrical Network, Exponential Decay

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13 Jun 2014

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7b practice quiz: exponential change (this is a former quiz: shown to the right is an electric circuit made up of a capacitor, a resistor, and a switch. When the switch is closed, at t = 0, there is a clockwise current in the circuit. The slope at t=0. 2s looks to be about: 1. 5v/0. 75s = -2v/s, which is about 2s-1 times the voltage at that point. The slope at t=1. 5s looks to be about: 0. 4v/2s = -0. 2v/s which is also about 2s-1 times the voltage at that point: without using any equations, briefly explain why vr decreases as time passes. As the charge drains from the capacitor, the voltage difference (which is proportional to the charge on it) across it diminishes. The voltage drops around the full circuit sum to zero, so as the voltage difference across the capacitor goes down, so does the voltage drop across the resistor.

Related Questions

? In Fig. 18.11b (same figure for 7th and 6th edition), the switch is closed at and the capacitor begins to charge. What is the voltage across the resistor and across the capacitor, expressed as fractions of (to two significant figures), (a) just after the switch is closed, (b) after two time constants have elapsed, and (c) after many time constants have elapsed?

This set of problems is designed to help you prepare for the lab oncapacitors. Here are some things you should know.
The charge on a capacitor is proportional to the voltage. Theconstant of proportionality is the capacitance:
q=VC.
The simplest type of capacitor is a parallel plate capacitorconsisting of twoparallel conducting plates...DUH. If the plateseach have area A and
are separated by a distance d, the capacitance will be
C=Ke0A/d,
where e0 is the permittivity of free space (you measured that lastweek) and K is the dielectric constant of what ever material isbetween the plates. If the space between the plates is filled withvacuum, the dielectric constant is exactly 1. Air is pretty darnclose to 1.
When a capacitor is charged in a series circuit with a resistor,the charge builds up with time. Consider the circuit below.

When the switch, S, is thrown to position A, the battery, withvoltage V0, will supply a current through the resistor, R, thatcharges the capacitor C. The voltage across the capacitor at anygiven time is given by
V=V0(1-e-t/RC).
The product RC is known as the time constant. After waiting a timeequal to 1 time constant, the voltage on the capacitor is(1-e-1)=0.632 of V0. After 5RC the capacitor is nearly fullycharged and has a voltage of 0.993V0. Eventually, the voltagebuilds up to V0.
When the switch is thrown to position B, the capacitor willdischarge through the resistor. The voltage as a fuction of timewill be given by
V=V0(e-t/RC).
After a long enough time, the capacitor will fully discharge theresistor.

1. [1pt]
A parallel plate capacitor has plates with length and width of 5.7cm and are separated by 7.0 mm. The capacitance is measured to be1.479Ã10-11 F. What is the dielectric constant of the materialbetween the plates?

Correct, computer gets: 3.60

2. [1pt]
Consider a series circuit like the one shown above with a resistorof R=80. kilo-ohms and a capacitor of C=8.0 uF. What is the timeconstant of the circuit?

Correct, computer gets: 0.64 s

Hint: Don't forget to convert to Farads and ohms from uF andkilo-ohms.
3. [1pt]
If the battery has a voltage of 12 V, what is the voltage acrossthe capacitor after the switch has been in position A for 2 timeconstants?

Correct, computer gets: 10.38 V
4. [1pt]
What is the final charge on the capacitor after a long time?

Correct, computer gets: 9.60E-05 C
5. [1pt]
Now let's say that the capacitor has been fully charged and wethrow the switch to position B. How long will it take for thevoltage on the capacitor to be 0.891 V?

6. [1pt] What is the charge on the capacitor at this time?

Answer: ____________

This set of problems is designed to help you prepare for the lab oncapacitors. Here are some things you should know.
The charge on a capacitor is proportional to the voltage. Theconstant of proportionality is the capacitance:
q=VC.
The simplest type of capacitor is a parallel plate capacitorconsisting of twoparallel conducting plates...DUH. If the plateseach have area A and
are separated by a distance d, the capacitance will be
C=Ke0A/d,
where e0 is the permittivity of free space (you measured that lastweek) and K is the dielectric constant of what ever material isbetween the plates. If the space between the plates is filled withvacuum, the dielectric constant is exactly 1. Air is pretty darnclose to 1.
When a capacitor is charged in a series circuit with a resistor,the charge builds up with time. Consider the circuit below.

When the switch, S, is thrown to position A, the battery, withvoltage V0, will supply a current through the resistor, R, thatcharges the capacitor C. The voltage across the capacitor at anygiven time is given by
V=V0(1-e-t/RC).
The product RC is known as the time constant. After waiting a timeequal to 1 time constant, the voltage on the capacitor is(1-e-1)=0.632 of V0. After 5RC the capacitor is nearly fullycharged and has a voltage of 0.993V0. Eventually, the voltagebuilds up to V0.
When the switch is thrown to position B, the capacitor willdischarge through the resistor. The voltage as a fuction of timewill be given by
V=V0(e-t/RC).
After a long enough time, the capacitor will fully discharge theresistor.

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For multiple choice questions, enter the letter corresponding tothe correct answer.

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1. [1pt]
A parallel plate capacitor has plates with length and width of 5.7cm and are separated by 7.0 mm. The capacitance is measured to be1.479Ã10-11 F. What is the dielectric constant of the materialbetween the plates?

Correct, computer gets: 3.60

Hint: Don't forget to convert distances to meters.

--------------------------------------------------------------------------------

2. [1pt]
Consider a series circuit like the one shown above with a resistorof R=80. kilo-ohms and a capacitor of C=8.0 uF. What is the timeconstant of the circuit?

Correct, computer gets: 0.64 s

Hint: Don't forget to convert to Farads and ohms from uF andkilo-ohms.
3. [1pt]
If the battery has a voltage of 12 V, what is the voltage acrossthe capacitor after the switch has been in position A for 2 timeconstants?

Correct, computer gets: 10.38 V
4. [1pt]
What is the final charge on the capacitor after a long time?

Correct, computer gets: 9.60E-05 C
5. [1pt]
Now let's say that the capacitor has been fully charged and wethrow the switch to position B. How long will it take for thevoltage on the capacitor to be 0.891 V?

Answer:

6. [1pt]
What is the charge on the capacitor at this time?

Answer:

PHY 7B Study Guide - Quiz Guide: Electrical Network, Exponential Decay

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