Physics 112 Formulae
area of circular ring of radius r and thickness dr=2 π r dr
volume of "meat" of cylindrical shell of length L, radius r, thickness dr=2 π r L dr
volume of "meat" of spherical shell of radius r and thickness dr=4 π r2 dr
UNIT 2: Potential Energy, Voltage, Capacitors
∆PE=qo∆V or PE=qoV
PE=U=kq0q1r01=14πεo q0q1r01, V=kq0r0=14πεo q0r0 (V→0 as r→∞);
PE=U=q04πεo q1r1+q2r2+q3r3+…, V=14πεo q1r1+q2r2+q3r3+… (V→0 as r→∞);
PE=q04πεoabdqr, V=14πεoifdqr V→0 as r→∞;
PEb-PEa=-abF∙dl=-abq0E∙dl; Vb-Va=-abE∙dl;
Infinite sheet: V=Ed
Q=CV; for parallel plates, C=Aεod;
PE=12CV2=Q22C=12QV;
Ceq=C1+C2+…; 1Ceq=1C1+1C2+…;
Cnew=KCold;
UNIT 3: Current, Resistance, Introduction to Circuits
I=dQdt=nqvdA; J=IA=nqvd; J=nqvd;
Ohm’s Law: E=ρJ and V=IR; R=ρLA;
P=IV=I2R=V2R;
Req=R1+R2+R3+…; 1Req=1R1+1R2+1R3+…;
Iin=Iout; closed loop∆V=0;
Charging: Qt=Qf1-e-tRC=CVo1-e-tRC; It=VoRe-tRC;
Discharging: Qt=Qoe-tRC; It=QoRCe-tRC;
Physics 112 – Test #3
24 October 2016
Name ______
Directions: This is a CLOSED BOOK test, and you may only use the calculator and cheat sheet provided. SHOW ALL OF YOUR REASONING! You can only get partial credit for an incorrect answer if you show your reasoning. You may have as much time as you like to finish this exam.
1. Consider two wires. Each is made out of pure silver.
Wire A has a radius r and length L.
Wire B has a radius 2r and length 2L.
a) (5 pts) Which one has the greater resistance (or are they both the same), and why?
b) (5 pts) If a 2V battery is connected across each, which has the greater current density?
2. (9 pts) Describe, using a physical picture of what is happening (with its flaws and all), why a wire gets hot when you put a current through it. Address why it gets hotter faster when you put more current through it.
3. Consider the circuit at below. The lone battery is ideal.
a) (15 pts) Determine the equivalent resistance the battery “sees”.
b) (15 pts) If the voltage at point a is 0V, determine the voltage at point b.
4. (20 pts) Use Kirchhoff’s Laws to set up the equations you would need to determine the current in each segment of the below circuit. DO NOT SOLVE THEM—just set them up correctly. Make sure you have enough equations!
5. The 1Ω resistor represents the internal resistance of the battery. Determine what V1 reads with the switch closed if:
a) (7 pts) the voltmeters and ammeter are ideal; and
b) (14 pts) if the voltmeters each have an internal resistance of 50Ω and the ammeter has an internal resistance of 5Ω.
6. (10 points) In the circuit shown at right, the capacitor is originally uncharged with the switch open. At t = 0 the switch is closed. After the switch is closed, the capacitor begins to charge up. Determine the value of C necessary to make the capacitor 1 electron short of being fully charged in 1 second.
BONUS BRAIN BUSTER!!! (+5 points)
A non-ideal battery (voltage of ideal voltage source within has voltage V, internal resistance r) is connected to a light bulb with resistance R as shown in the diagram below. What must the resistance R of the light bulb be (in terms of r) in order to make it shine brightest? (This is called the “ideal load”.)
Credit will only be given for correct reasoning. If you are able to guess the correct answer but give no correct reasoning, you will receive no extra credit. However, if you give some correct reasoning that would (or does) lead to the correct answer, at least some credit will be given.
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By signing my name above, I affirm that this test represents my work only, without aid from outside sources. In all aspects of this course I perform with honor and integrity.