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Physics 2102 Jonathan Dowling. b. a. Physics 2102 Lecture 11. DC Circuits. Incandescent light bulbs. Which light bulb has a smaller resistance: a 60W, or a 100W one? Is the resistance of a light bulb different when it is on and off?

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physics 2102 lecture 11

Physics 2102

Jonathan Dowling

b

a

Physics 2102 Lecture 11

DC Circuits

incandescent light bulbs
Incandescent light bulbs
  • Which light bulb has a smaller resistance: a 60W, or a 100W one?
  • Is the resistance of a light bulb different when it is on and off?
  • Which light bulb has a larger current through its filament: a 60W one, or a 100 W one?
  • Would a light bulb be any brighter if used in Europe, using 240 V outlets?
  • Would a US light bulb used in Europe last more or less time?
  • Why do light bulbs mostly burn out when switched on?
emf devices and single loop circuits

b

a

i

- +

c

d

b

a

i

iR

E

Va

a

b

c

d=a

EMF devices and single loop circuits

The battery operates as a “pump” that moves

positive charges from lower to higher electric potential. A battery is an example of an “electromotive force” (EMF) device.

These come in various kinds, and all transform one source of energy into electrical energy. A battery uses chemical energy, a generator mechanical energy, a solar cell energy from light, etc.

The difference in potential energy that the

device establishes is called the EMF

and denoted by E.

E = iR

circuit problems
Circuit problems

Given the emf devices and resistors in a circuit, we want to calculate the circulating currents. Circuit solving consists in “taking a walk” along the wires. As one “walks” through the circuit (in any direction) one needs to follow two rules:

When walking through an EMF, add +Eif you flow with the current or -E

otherwise. How to remember: current “gains” potential in a battery.

When walking through a resistor,add -iR, if flowing with the current or +iR

otherwise. How to remember: resistors are passive, current flows “potential down”.

Example:

Walking clockwise from a: + E-iR=0.

Walking counter-clockwise from a: - E+iR=0.

ideal batteries vs real batteries
Ideal batteries vs. real batteries

If one connects resistors of lower and lower value of R to get higher and higher currents, eventually a real battery fails to establish the potential difference E, and settles for a lower value.

One can represent a “real EMF device” as an ideal one attached to a resistor,

called “internal resistance” of the EMF device:

E –i r -i R=0  i=E/(r+R)

The true EMF is a function of current: the more current we want, the smaller Etruewe get.

Etrue = E –i r

resistors in series and parallel

Resistors in series and parallel

An electrical cable consists of 100 strands of fine wire, each having 2 W resistance. The same potential difference is applied between the ends of all the strands and results in a total current of 5 A.

  • What is the current in each strand?Ans: 0.05 A
  • What is the applied potential difference?Ans: 0.1 V
  • What is the resistance of the cable?Ans: 0.02 W

Assume now that the same 2 W strands in the cable are tied in series, one after the other, and the 100 times longer cable connected to the same 0.1 Volts potential difference as before.

  • What is the potential difference through each strand?Ans: 0.001 V
  • What is the current in each strand?Ans: 0.0005 A
  • What is the resistance of the cable?Ans: 200 W
  • Which cable gets hotter, the one with strands in parallel or the one with strands in series?Ans: each strand in parallel dissipates 5mW (and the cable dissipates 500 mW); each strand in series dissipates 50 mW (and the cable dissipates 5mW)
dc circuits resistances in series
DC circuits: resistances in series

Two resistors are “in series” if they are connected such that the same current flows in both.

The “equivalent resistance” is a single imaginary resistor that can replace the resistances in series.

“Walking the loop” results in :E –iR1-iR2-iR3=0  i=E/(R1+R2+R3)

In the circuit with the equivalent resistance, E –iReq=0  i=E/Req

Thus,

multiloop circuits resistors in parallel
Multiloop circuits: resistors in parallel

Two resistors are “in parallel” if they are connected such that there is the same potential drop through both.

The “equivalent resistance” is a single imaginary resistor that can replace the resistances in parallel.

“Walking the loops” results in :E –i1R1=0, E –i2R2=0, E –i3R3=0

The total current delivered by the battery is i = i1+i2+i3 = E/R1+ E/R2+ E/R3.

In the circuit with the equivalent resistor,

i=E/Req. Thus,

resistors and capacitors
Resistors and Capacitors

ResistorsCapacitors

Key formula: V=iR Q=CV

In series: same current same charge

Req=∑Rj 1/Ceq=∑1/Cj

In parallel: same voltage same voltage

1/Req=∑1/Rj Ceq=∑Cj

example

Bottom loop: (all else is irrelevant)

12V

8W

Example

Which resistor gets hotter?

example1
Example
  • Which circuit has the largest equivalent resistance?
  • Assuming that all resistors are the same, which one dissipates more power?
  • Which resistor has the smallest potential difference across it?
example2
Example

Find the equivalent resistance between points

(a) F and H and

(b) F and G.

(Hint: For each pair of points, imagine that a battery is connected across the pair.)

monster mazes
Monster Mazes

If all capacitors have a capacitance of 6mF, and all batteries are ideal and have an emf of 10V, what is the charge on capacitor C?

If all resistors have a resistance of 4W, and all batteries are ideal and have an emf of 4V, what is the current through R?