Electricity

Calculate the potential difference between the two ends of the wire.

potential difference = ______ $\text{V}$

Show that the cross-sectional area of the wire is $1.3 \times 10^{-6}\ \text{m}^{2}$.

Show that the number density of charge carriers in the wire is $8.3 \times 10^{28}\ \text{m}^{-3}$.

Calculate the average drift speed of the charge carriers (electrons) in the wire.

average drift speed = ______ $\text{m s}^{-1}$

State and explain how the resistance of wire Q compares with the resistance of wire P.

On Fig. 6.3, sketch a graph of the variation of the average drift speed of the charge carriers with distance from end X of wire Q.

State and explain the effect, if any, on the resistance of a filament wire in a lamp as the current in the wire decreases.

On Fig. 5.1, sketch the $I-V$ characteristic of a filament lamp.

Calculate the e.m.f. $E$ of the battery.

$E$ = ______ $\text{V}$

The filament wire of lamp B has a cross-sectional area of $1.4 \times 10^{-9}\text{ m}^2$. The number of free (conduction) electrons per unit volume in the metal of the filament wire is $3.4 \times 10^{28}\text{ m}^{-3}$.

Calculate the average drift speed of the free electrons in the filament wire of lamp B.

average drift speed = ______ $\text{m s}^{-1}$

The current in a filament lamp decreases.

State and explain how the resistance of the lamp changes.

the current in the wire

current = ______

the average drift speed of the free electrons

average drift speed = ______

the average time taken for a free electron to move along the full length of the wire.

time taken = ______

the current in the resistance wire

current = ______ $\text{A}$

the number of free electrons that pass through the resistance wire in a time of $50\text{ s}$

number = ______

the resistance of the wire.

resistance = ______ $\Omega$

The metal of the resistance wire in the circuit has a resistivity of $1.4 \times 10^{-6}\ \Omega\text{m}$. The cross-sectional area of the wire is $0.25\text{ mm}^2$.

Determine the length of the wire.

length = ______ $\text{m}$

The circuit shown in Fig. 6.1 is modified by replacing the original resistance wire with a second resistance wire. The second wire has a greater diameter than the original wire. There are no other differences between the second wire and the original wire.

By reference to resistance, state and explain whether the power dissipated by the second wire is more than, less than or the same as the power dissipated by the original wire.

The circuit shown in Fig. 6.1 is modified by connecting a second battery, of e.m.f. $8.0\text{ V}$ and negligible internal resistance, in parallel with the original battery and the original resistance wire, as shown in Fig. 6.2.

By reference to the current in the resistance wire, state and explain whether the addition of the second battery causes the power in the original resistance wire to decrease, increase or stay the same.

State Ohm’s law.

State how Fig. 5.1 shows this.

Explain why the resistance varies in this way.

the current in lamp P

current = ______ $\text{A}$

the total power dissipated in lamps P and Q

total power = ______ $\text{W}$

the resistance of the potentiometer between its ends A and B.

resistance = ______ $\Omega$

The slider of the potentiometer in (c) is moved to end A.

State and explain the effect on the brightness of lamps P and Q.

lamp P: ______

lamp Q: ______

Calculate the charge passing through the cell in a time of $7.5$ minutes.

charge = ______ $\text{C}$

Calculate the percentage efficiency with which the cell supplies power to wire X.

efficiency = ______ $\%$

the number density $n$ of the free electrons

$n$ = ______ $\text{m}^{-3}$

the average drift speed of the free electrons.

average drift speed = ______ $\text{m s}^{-1}$

A wire Y has the same cross-sectional area as wire X and is made of the same metal. Wire Y is longer than wire X.

Wire X in the circuit is now replaced by wire Y. Assume that wire Y has the same temperature as wire X.

State and explain whether the average drift speed of the free electrons in wire Y is greater than, the same as, or less than that in wire X.

State what is meant by the symbols $A$ and $n$.

$A$: ______
$n$: ______

Use the above expression to determine the SI base units of $e$.
Show your working.

base units ______

Two lamps P and Q are connected in series to a battery, as shown in Fig. 6.1.

The radius of the filament wire of lamp P is twice the radius of the filament wire of lamp Q. The filament wires are made of metals with the same value of $n$.

Calculate the ratio

ratio = ______

Define resistance.

A potential difference of $0.60\ \text{V}$ is applied across a resistor of resistance $4.0\ \text{G}\Omega$.

Calculate the current, in $\text{pA}$, in the resistor.

current = ______ $\text{pA}$

The energy $E$ transferred when charge $Q$ moves through an electrical component is given by the equation

where $V$ is the potential difference across the component.

Use the equation to determine the SI base units of potential difference.

SI base units ______

Define electric potential difference (p.d.).

The variation with potential difference $V$ of the current $I$ in a semiconductor diode is shown in Fig. 6.1.

Use Fig. 6.1 to describe qualitatively the variation of the resistance of the diode as $V$ increases from 0 to $1.0\ \text{V}$.

Use Fig. 6.1 to determine the resistance of the diode.

resistance = ______ $\Omega$

Calculate:

1. the resistance of X

resistance = ______ $\Omega$

1. the ratio

ratio = ______

Define the volt.

Use Fig. 6.2 to determine the current in the battery. Explain your working.

current = ______ $\text{A}$

Calculate the resistance of resistor R.

resistance = ______ $\Omega$

The filament wires of the two lamps are made from material with the same resistivity at their operating temperature in the circuit. The diameter of the wire of lamp P is twice the diameter of the wire of lamp Q.

Determine the ratio

ratio = ______

The filament wire of lamp Q breaks and stops conducting.

State and explain, qualitatively, the effect on the resistance of lamp P.