Electricity：練習問題

An electric current of $$0.50 \text{ A}$$ flows through a resistor when a potential difference of $$12 \text{ V}$$ is applied across it. What is the resistance of the resistor?

A uniform resistance wire of length \( L \) and cross-sectional area \( A \) has a resistance \( R \). The wire is stretched such that its length increases by \( 10\% \) while its volume remains constant. What is the new resistance of the wire in terms of \( R \)?

A uniform resistance wire of length \(L\) and resistance \(R\) is stretched such that its length becomes \(1.5L\) while its volume remains constant. This stretched wire is then cut into three equal lengths, and the three pieces are connected in parallel. What is the total resistance of this parallel combination?

Which statement correctly describes the behavior of a thermistor with a negative temperature coefficient?

A metal wire X has a radius \( r \) and a length \( L \). Another wire Y of the same material has a radius \( 2r \) and a length \( 2L \). The two wires are connected in series to a power supply. What is the ratio of the average drift velocity of the free electrons in wire X to that in wire Y?

A constant current of $$2.5\, A$$ flows through a wire for $$120\, s$$. Calculate the total charge that passes through a cross-section of the wire.

A wire of length $$2.0\, m$$ and cross-sectional area $$1.0 \times 10^{-7}\, m^2$$ has a resistance of $$4.0\, \Omega$$. Calculate the resistivity of the material.

A simple circuit consists of a 12 V power supply with negligible internal resistance connected to two resistors, R₁ and R₂, in series. Resistor R₁ has a resistance of 4.0 Ω and resistor R₂ has a resistance of 8.0 Ω.

(a) Calculate the total resistance of the circuit.
(b) Determine the total current flowing through the circuit.
(c) Calculate the potential difference across resistor R₁.
(d) Determine the power dissipated by resistor R₂.

(a) Define resistivity and state its SI base units.
(b) A uniform wire has a length of \(1.5 \text{ m}\) and a radius of \(0.40 \text{ mm}\). The resistance of the wire is measured to be \(2.2 \, \Omega\). Calculate the resistivity of the material of the wire.
(c) The wire is now stretched so that its length increases to \(3.0 \text{ m}\) while its volume remains constant. Determine the new resistance of the wire.