Electricity：練習問題

In the expression for the electric current in a conductor, \( I = Anvq \), what are the SI base units for the number density \( n \) of the charge carriers?

As the potential difference \( V \) across a filament lamp increases, the temperature of its filament also increases.
How do the resistance of the lamp and the gradient of its \( I \)–\( V \) characteristic graph change as \( V \) increases?

Two wires, P and Q, are made of different metals. Wire P has twice the length and half the diameter of wire Q. The resistivity of the metal in wire P is half that of the metal in wire Q.
The two wires are connected in parallel to a power supply of constant potential difference. What is the ratio \(\frac{\text{power dissipated in P}}{\text{power dissipated in Q}}\)?

A constant current of \( 0.50\text{ A} \) flows through a circuit for a time of \( 2.0\text{ minutes} \).
What is the total charge that flows past a point in the circuit during this time?

Two wires, 1 and 2, are made of the same metal and are connected in series. The diameter of wire 1 is three times the diameter of wire 2.
What is the ratio \(\frac{\text{mean drift velocity of electrons in wire 1}}{\text{mean drift velocity of electrons in wire 2}}\)?

Define the potential difference across an electrical component in terms of the energy transferred and the electrical charge.

The drift velocity of free electrons in a copper wire is \( v \). A second copper wire has half the diameter of the first wire but carries the same current.
Determine the drift velocity in the second wire in terms of \( v \).

A uniform wire of resistance \( R \) is stretched uniformly until its length is doubled.
Assuming the volume and resistivity of the material remain unchanged, determine the new resistance of the wire in terms of \( R \).

A battery provides a constant current of \( 0.40 \text{ A} \) to a small lamp for a time of \( 5.0 \text{ minutes} \).
(a) Calculate the total charge \( Q \), in coulombs, that passes through the lamp during this time.
(b) Determine the number of electrons that pass through the lamp, given that the elementary charge is \( 1.6 \times 10^{-19} \text{ C} \).

An electric heater is designed to operate at a potential difference of \( 230 \text{ V} \) and has a power rating of \( 1.5 \text{ kW} \).
(a) Calculate the resistance \( R \) of the heating element when it is operating at its rated power.
(b) The heating element is made of a wire with a cross-sectional area of \( 2.5 \times 10^{-7} \text{ m}^2 \) and a resistivity of \( 1.1 \times 10^{-6} \ \Omega \text{ m} \). Calculate the length \( L \) of the wire required for this element.