Electricity: Physics 9702 (Cambridge International AS & A Level)

A phone charger delivers a constant current of $1.50\text{ A}$ to a battery for $40.0$ minutes.

(a) State the equation relating charge $Q$, current $I$ and time $t$, and use it to calculate the charge $Q$ delivered to the battery in this time. [2]

(b) The charge on a single electron is $e = 1.60\times10^{-19}\text{ C}$. Calculate the number $n$ of electrons that flow through the charger in this time. [2]

(c) State what is meant by an electric current, in terms of the charge carriers in a conductor. [1]

A student obtains the current–voltage (I–V) characteristic of an unknown electrical component at room temperature. As the potential difference $V$ across the component is increased steadily from zero, the current $I$ also increases, but not in direct proportion to $V$: for equal increases in $V$, the increase in $I$ becomes progressively smaller. The current never decreases and the graph never bends back on itself.

Which statement correctly explains this I–V characteristic?

A battery maintains a constant potential difference of $9.00\text{ V}$ across a resistor of resistance $15.0\,\Omega$. The circuit is switched on for $4.00$ minutes.

(a) State what is meant by potential difference. [1]

(b) Calculate the current $I$ in the resistor. [2]

(c) Calculate the charge $Q$ that flows through the resistor during the $4.00$ minutes. [2]

(d) The charge on a single electron is $e = 1.60\times10^{-19}\text{ C}$. Use $Q = ne$ to calculate the number $n$ of electrons that flow through the resistor in this time. [2]

(e) Calculate the power $P$ dissipated in the resistor using $P = VI$, and show that this agrees with the value obtained using $P = I^2R$. [2]

A wire is made from constantan, of resistivity $\rho = 4.90\times10^{-7}\,\Omega\,\text{m}$. The wire has length $L = 2.50\text{ m}$ and a uniform circular cross-section of diameter $0.460\text{ mm}$.

(a) Calculate the cross-sectional area $A$ of the wire, in $\text{m}^2$. [2]

(b) Calculate the resistance $R$ of the wire, using $R = \rho L / A$. [2]

(c) A second wire is made from the same constantan, with the same length, but with double the diameter of the first wire. State and explain, without further detailed calculation, how the resistance of the second wire compares with the resistance found in (b). [2]

(d) The original wire (from part (b)) carries a current of $0.600\text{ A}$. Calculate the power dissipated in the wire. [2]

A student measures the current $I$ through a component for four different values of potential difference $V$ across it:

Which statement correctly describes how the resistance of the component changes over this range, and what this suggests about the component?

A copper wire of uniform circular cross-section carries a current of $2.50\text{ A}$. The wire has diameter $0.60\text{ mm}$. Copper has $n = 8.5\times10^{28}$ free (conduction) electrons per cubic metre, and the charge on a single electron has magnitude $q = 1.60\times10^{-19}\text{ C}$.

(a) State the equation relating current $I$, cross-sectional area $A$, number density of charge carriers $n$, drift velocity $v$ and charge on each carrier $q$, and identify what is meant by "drift velocity". [2]

(b) Calculate the cross-sectional area $A$ of the wire, in $\text{m}^2$. [2]

(c) Calculate the drift velocity $v$ of the free electrons in the wire. [2]

(d) The current in the wire is increased to $5.00\text{ A}$, with $A$, $n$ and $q$ unchanged. State and calculate the new drift velocity. [2]

(e) The drift velocity found in (c) is extremely small, yet a lamp connected to this wire lights up almost instantly when the circuit is switched on. Explain why. [1]

A student connects a semiconductor diode into a circuit and measures the current $I$ through it for a range of potential differences $V$ across it, first with the diode forward-biased and then with the diode reverse-biased, in each case increasing the magnitude of $V$ from zero.

Which statement correctly describes the resulting I–V characteristic of the diode?

A thermistor is connected across a supply that maintains a constant potential difference of $6.00\text{ V}$ across it. At a temperature of $20\,^{\circ}\text{C}$, the thermistor has resistance $R_1 = 1200\,\Omega$. The thermistor is then warmed to a higher temperature, at which its resistance falls to $R_2 = 300\,\Omega$.

(a) Calculate the current $I_1$ in the thermistor at $20\,^{\circ}\text{C}$. [2]

(b) Calculate the current $I_2$ in the thermistor at the higher temperature. [2]

(c) Using the equation $I = Anvq$, explain, in terms of the charge carriers within the semiconductor material of the thermistor, why its resistance falls as its temperature rises. [3]

Two wires, X and Y, are made from the same material at the same temperature. Wire X has length $L$ and cross-sectional area $A$. Wire Y has length $2L$ (twice as long) and cross-sectional area $A/2$ (half as large).

How does the resistance of wire Y compare with the resistance of wire X?

An engineer is designing a heating element for a laboratory kettle, to be made from nichrome wire of resistivity $\rho = 1.10\times10^{-6}\,\Omega\,\text{m}$ and uniform cross-sectional area $A = 4.00\times10^{-8}\text{ m}^2$. The element must have resistance $R = 55.0\,\Omega$ when connected to the $230\text{ V}$ mains supply.

(a) Calculate the current $I$ that flows in the element when it is connected to the $230\text{ V}$ supply. [2]

(b) Calculate the length $L$ of nichrome wire needed to give the required resistance $R = 55.0\,\Omega$, using $R = \rho L / A$. [2]

(c) Calculate the power $P$ dissipated by the heating element when connected to the $230\text{ V}$ supply, using $P = V^2/R$. [2]

(d) The wire is now replaced by a nichrome wire of the same length but with half the cross-sectional area. State and explain the effect this has on the resistance and, hence, on the power dissipated at the same $230\text{ V}$ supply. [2]