PHY2054 Spring 2008
1
Prof. P. Kumar
Prof. P. Avery
March 5, 2008
Exam 2 Solutions
1.
Two cylindrical resistors are made of the same material and have the same resistance. The
resistors,
R
1
and
R
2
, have different radii,
r
1
and
r
2
, and different lengths,
L
1
and
L
2
. Which of the
following relative values for radii and lengths would result in equal resistances?
(1) 2
r
1
=
r
2
and 4
L
1
=
L
2
(2) 2
r
1
=
r
2
and
L
1
= 2
L
2
(3)
r
1
=
r
2
and 4
L
1
=
L
2
(4)
r
1
=
r
2
and
L
1
= 2
L
2
(5) none of these
The resistance is given by
/
R
L
A
ρ
=
, where
ρ
is the resistivity, L is the length and A is the cross
sectional area. To keep R unchanged, the ratio of L to A must be unchanged.
Since A =
π
r
2
, if r
is doubled then L must be multiplied by 4. Only the answer (1) works.
2.
If a 9.0-V battery with internal resistance 0.2
Ω
and an 18
Ω
resistor are connected together,
what is the amount of electrical energy (in J) transformed to heat per coulomb of charge that
flows through the circuit?
(1) 9.0
(2) 3.0
(3) 0.50
(4) 72
(5) 4.5
The amount of heat released is P
Δ
t, where P = Vi.
The total amount of charge is q = i
Δ
t.
Thus
the amount of heat energy released per coulomb of charge is P
Δ
t / i
Δ
t = P/i = V = 9V.

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