3. E
The resistance for a wire is given by the formula R =
?
L/A, where
?
is the resistivity of the material the wire is made of,
L is the length of the wire, and
A is the cross-sectional area of the
wire.
The value of
?
varies from material to material, so the material the wire is made of does
affect the resistance in the wire, which is why we don’t wire our houses with
glass or wooden wires. The length of the wire,
L, also affects the resistance, since the longer a wire gets, the
farther the electrons in the wire have to travel. The cross-sectional area,
A, and hence the diameter of the
wire affects the resistance, since charges have more room to move in a wider
wire. Since all three of the statements are true, the answer is E.
4. B
According to Ohm’s Law, V = IR:
current is directly proportional to potential difference. If the potential
difference across
R1
is half the potential difference across
R2,
and if
R1
and
R2
have the same resistance, then the current through
R1
is half the current through
R2.
5. B
The equivalent resistance,
R1,
of two identical resistors in parallel is given by the formula:
The equivalent resistance of three identical resistors in parallel is given by
the formula:
The ratio, then, between the new resistance and the old is:
6. D
According to Ohm’s Law, V = IR,
current and resistance are inversely proportional. In the previous question, we
saw that the new resistance is
2 /3 the old resistance. That means that,
inversely, the new current is
3 /2 times the old resistance.
7. E
The power dissipated in a resistor is given by the formula
P = I2R, which in
this case has a value of 20 W. The heat
dissipated in a resistor is given by the formula
H = Pt: every second, the resistor dissipates
20 J of heat. Since we are looking at a
10-second period, the total heat dissipated
is 200 J.
8. A
The equivalent capacitance of two capacitors in series is:
The equivalent capacitance of two capacitors in parallel is simply the sum of
the two capacitors, so
Ct = C1 + C2
= 2C. The ratio between the
equivalent capacitance of the two capacitors in series and the two capacitors in
parallel is therefore:
9. C
The energy stored in a capacitor is
U = 1/2 C(?V)2.
When a dielectric with a dielectric constant of
?
is inserted between the plates of a capacitor with capacitance
C, the new capacitance is
?
C. So (C) is the correct answer.
10. D
When the dielectric is inserted, the electrons in it create an electric field
that opposes the field between the plates of the capacitor. Since electric field
and potential difference are directly proportional, this decrease in the
electric field causes a decrease in the potential difference.
The energy stored in a capacitor is given by the equation
U = (1/2)Q?V,
so a decrease in the potential difference also leads to a decrease in the stored
energy.
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Practice Questions
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