DC Circuits

NAME:

____________________________________

NAME:

____________________________________

NAME:

____________________________________

RECITATION SECTION:

__________________________

INSTRUCTOR:

__________________________

DATE:

__

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This activity is based on the following concepts:

The power delivered by an EMF source is given by

i

ε

.

The power dissipated by a

single

resistor is given by

iV

, where

V

is the potential drop

across

just

that

resistor.

For resistances in series: the net resistance is equal to the sum of all resistances in series:

For resistances in

parallel: the net reciprocal resistance is equal to the sum of all

reciprocal resistances in parallel:

The loop rule:

o

Follow a closed loop around any circuit; the sum of

all

the changes in potential that

you encounter must

equal

ze

ro.

The junction rule:

o

The algebraic sum of currents at a junction in a circuit must equal zero.

Exercise 1

The circuits shown below are all constructed using identical bulbs of resistance

R

and ideal

batteries of EMF

ε

. Assume for simplicity that the resistance of a bulb does not depend on the

temperature of its filament (in reality, of course, it does depend upon this).

Q1.

Rank the circuits in order of increasing power supplied by th

e battery

, defending your

ranking with physical reasoning or a calculation

.

(

Hint

: the battery provides exactly the same

emf

ε

in each of the four circuits, but the current provided by the battery in each case is

dependent upon the total resistance in the

circuit.)

+

−

+

−

+

−

+

−

A

B

C

D

X

X

X

X

Q2.

In each of the four circuits, a bulb has been labeled '

X

'. Rank the circuits above according to

how bright bulb '

X

' is, in order of increasing brightness. (Assume that the brightness of the bulb

is directly proportional to the

power it diss

i

pates.) Again,

defend your ranking based on a clear

statement of your physical reasoning or a calculation which supports your claim.

Exercise 2

Consider the circuit shown below. Use the junction and loop rules to

set up a system of equations

that would allow you to

determine the currents through the three resistors.

Be sure to label the

figure with your expectation as to which

direction

each current

flows through the resistors

.

(

Optional

: if time permits, solve you

r system of equations for the current through each resistor.)

+

−

+

−

+

−

20 Ω

㤠9

10 Ω

㤠9

20 Ω

㤠9

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