Lab #4: RC and RL Circuits

• remember what capacitors and inductors are

• remember why circuits containing them can have currents that change with time

Capacitor

Two plates with a dielectric in between

0 0

1

dV Ed d Q

A

V QC

RC Circuit: close switchCharge will flow to the capacitor, charging it and raising its potential. The potential will asymptotically approach V0. The current will be biggest at the beginning, whenV is greatest, and will get smaller as V decreases (as the cap charges).

/0

/0

/0

/0

(1 )

/ (1 )

t RC

t RCC

t RC

t RCR

Q CV e

V Q C V e

dQ VI e

dt R

V IR V e

RC time constant (): time for cap to charge to .63 of VoCurrent to drop to .37 of max value

Note: Vc+vr= constant!

RC Circuit: Open Switch

/ /00

/0

t RC t RC

t RC

VI I e e

R

V IR V e

Discharge with same RC time constant

Experiment• Be careful with the grounds! Outer shield on bnc cable from scope is at ground. Make sure it goes on ground side of cap when measuring it

• instrumentation amplifier: needed when measuring voltage across R

• calculate RC from the values in the circuit

•measure the RC time constant (), which is the time to drop to 0.37% of maximum signal and compare

Inductor

Sprague-Goodman

A coil of wire

dIV L

dt

Minus sign means sense of the voltage will be to oppose the change in current.

Inductors

Instead of a step function change in voltage, the inductor will develop a voltage across it due to the change in current which will partially cancel the voltage in the battery and reduce the current.

/( / )

/( / )(1 )

t L RL B

t L RR B

V V e

V V e

/( / )(1 )t L RBVi e

R

L/R time constantExperiment: similar to first part, but with L/R circuit

174 refresherIf you have made two measurements of the same thing, how do you check to see if they agree within errors -> Is their difference zero within errors?

1 2

1 2

1 2

1 2

2 2

2

2 1 2

theory: 0

0

x x

d x x

d

x x

x x

x x

Calculate chi2 and prob of having a difference that big or bigger…

Sqrt(12)

22RMS x x

0x

When you have an LSB, what is the random error?

Imagine a step with width a centered at zero.

Remember:

/2/2 32

22 /2 /2

3

12

/ 12

aa

a a

xx dx

ax

a a

RMS a

Hints• When wiring circuit, use black wires only for portions of

circuit at ground.• When wiring the circuit, first wire everything except the

scope. Add it last.• Be sure scope is DC coupled (AC coupling adds an extra

capacitor, beyond the one you want to measure)• make sure ch1 and ch2 are on x1 setting• Make sure they have the same v/division scale• When you measure R, L, and C, make sure they are not

still in the circuit. If you put an ohm meter across a resistor in a circuit, you measure the resistance of the circuit, not of the resistor, etc.

• Don’t really need an external trigger for this lab. Can trigger off signal itself.

Hints• lab starts pg 39 • Only 6 lcr meters in class. They come in two different types. For systematic errors, see manual on your desk top (be careful to use the correct one). Only consider systematic errors in L,R and C measurements, not in scope measurements • for A-1, replace 2nd sentence with “Capture both waveforms using wavestar. Then sketch Vin-Vc and show to your instructor.• capture VR in A-2. Be sure to use the instrumentation amplifier when measuring VR• when calculate lifetime, need an error• for example, in A-3, need to calculate errors and say if they are consistent within errors• A-4. don’t try higher frequencies. Just lower ones.

• A-4. How does the time constant change with frequency? Does it agree with expectations to within errors? (ignore the sentence “consider the fact…”

Hints

• DO NOT DO SECTION B.3