D.C. Circuits

Determine $R$.

$R$ = ______ $\Omega$

Explain why the potential difference $V$ between any two points on wire XY is proportional to the distance $L$ between those points.

Calculate $E$.

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

The value of $R$ is now decreased.

State and explain the change that must be made to the position of P on wire XY so that the galvanometer reads zero again.

State Kirchhoff’s first law.

A cell with internal resistance $r$ is connected to two resistors of resistances $R_1$ and $R_2$ as shown in Fig. 6.1.

The potential differences (p.d.s) across $R_1$ and $R_2$ are $V_1$ and $V_2$ respectively.
The terminal p.d. across the cell is $V$.
The current in the circuit is $I$.

Use Kirchhoff’s laws to show that the total resistance $R_T$ of the external circuit is given by

The electromotive force (e.m.f.) of the cell in Fig. 6.1 is $1.50\text{ V}$.

The values of $R_1$ and $R_2$ are $10\ \Omega$ and $15\ \Omega$ respectively. The terminal p.d. of the cell is $1.35\text{ V}$.

Calculate the internal resistance $r$ of the cell.

$r$ = ______ $\Omega$

the current in the cell

the terminal p.d. of the cell.

State Kirchhoff’s second law.

The current in the circuit is $1.1 \times 10^{-2}\ \text{A}$. The potential difference across $Y$ is $4.0\ \text{V}$.

Calculate the resistance of $X$.

resistance = ______ $\Omega$

The temperature of $Y$ is changed to $190^\circ\text{C}$. The resistance of $X$ remains unchanged.

Determine the new potential difference across $Y$.

potential difference = ______ $\text{V}$

The resistance of $X$ is increased. The temperature of $Y$ remains at $190^\circ\text{C}$.

By reference to the current in the circuit, state and explain the effect of this change, if any, on the potential difference across $Y$.

Show that the current $I$ in the circuit is $0.50\text{ A}$.

Calculate the combined resistance of the two resistors.

resistance = ______ $\Omega$

Use your answer in (a)(ii) to determine resistance $R$.

$R$ = ______ $\Omega$

On Fig. 7.2, complete the circuit diagram to show this arrangement.

Explain, without calculation, whether the terminal p.d. across the cell is now less than, equal to or greater than $1.36\text{ V}$.

A battery of electromotive force (e.m.f.) $9.0\ \text{V}$ and negligible internal resistance is connected to a light-dependent resistor (LDR) and a fixed resistor, as shown in Fig. 7.1.

The LDR and fixed resistor have resistances of $1800\ \Omega$ and $1200\ \Omega$ respectively.

Calculate the potential difference across the LDR.

potential difference = ______ $\text{V}$

Calculate the length XZ along the resistance wire.

length XZ = ______ $\text{m}$

The environmental conditions change causing a decrease in the resistance of the LDR. The temperature of the LDR remains constant.

State whether there is a decrease, increase or no change to:

• the intensity of the light illuminating the LDR
• the total power produced by the battery
• the length XZ so that the galvanometer reads zero.

Show that the current in the battery is $0.050\ \text{A}$.

Calculate the resistance of the LDR.

resistance = ______ $\Omega$

Determine the ratio

ratio = ______

The intensity of the light incident on the LDR increases.

State and explain what happens to the voltmeter reading.

A network of three resistors of resistances $R_1$, $R_2$ and $R_3$ is shown in Fig. 6.1.

The individual potential differences across the resistors are $V_1$, $V_2$ and $V_3$. The current in the combination of resistors is $I$ and the total potential difference across the combination is $V$.

Show that the combined resistance $R$ of the network is given by

Switch X is open.

Calculate the potential difference across $R_1$.

potential difference = ______ $\text{V}$

Switch X is now closed. The resistance of the thermistor is $12.0\ \text{k}\Omega$.

Calculate the current in the battery.

current = ______ $\text{A}$

The switch X in the circuit in (b) remains closed. The temperature of the thermistor decreases.

By reference to the current in the battery, state and explain the effect, if any, of the decrease in temperature on the power produced by the battery.

Define the electromotive force (e.m.f.) of a source.

The circuit shown in Fig. 5.1 contains a battery of e.m.f. $E$ that has internal resistance $r$, a variable resistor, a voltmeter and an ammeter.

Readings from the two meters are taken for different settings of the variable resistor. The variation with current $I$ of the potential difference (p.d.) $V$ across the terminals XY of the battery is shown in Fig. 5.2.

Explain why $V$ is not constant.

the e.m.f. $E$

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

the maximum current that the battery can supply

maximum current = ______ $\text{A}$

the internal resistance $r$.

$r$ = ______ $\Omega$

On Fig. 5.2, sketch a line to show a possible variation with $I$ of $V$ for a battery with a lower e.m.f. and a lower internal resistance than the battery in (b). Your line should extend over at least the same range of currents as the original line.

Explain, in terms of energy and without a calculation, why the potential difference across the lamp must be less than the e.m.f. of the battery.

Calculate:

1. the current in the circuit

current = ______ $\text{A}$

1. the potential difference across the lamp

potential difference = ______ $\text{V}$

1. the internal resistance of the battery.

internal resistance = ______ $\Omega$

Sketch a circuit diagram showing how two of these three resistors may be connected together to give a combined resistance of $30\ \Omega$ between the terminals shown. Label the values of the resistances on your diagram.

A potential divider circuit is produced by connecting the three resistors to a battery of e.m.f. $9.0\ \text{V}$ and negligible internal resistance. The potential divider circuit provides an output potential difference $V_{\text{OUT}}$ of $3.6\ \text{V}$. The circuit diagram is shown in Fig. 6.2.

On Fig. 6.2, label the resistances of all three resistors and the potential difference $V_{\text{OUT}}$.

State Kirchhoff’s second law.

1. the combined resistance of the two resistors connected in parallel

combined resistance = ______ $\Omega$

1. the current in the battery.

current = ______ $\text{A}$

Show that the internal resistance $r$ is $2.5\ \Omega$.

Determine the ratio

ratio = ______

The battery in (b) is now connected to a battery of e.m.f. $7.2\text{ V}$ and internal resistance $3.5\ \Omega$. The new circuit is shown in Fig. 5.2.

Determine the current in the circuit.

current = ______ $\text{A}$