DC: Practical Circuits & Kirchhoff's Laws (CIE A Level Physics)

Three resistors of resistances R₁, R₂ and R₃ are connected as shown in Fig. 1.1.

The currents in the resistors are I₁, I₂ and I₃. The total current in the combination of resistors is I and the potential difference across the combination is V.

Show that the total resistance R of the combination is given by the equation

A battery of electromotive force (e.m.f.) 6.0 V and internal resistance r is connected to an external resistor of resistance 12 Ω and a thermistor X, as shown in Fig. 1.2.

Fig. 1.2

[1]

Calculate:

•   the total energy transferred by the battery

energy = ............................................................ J

•   the number of electrons that pass through the battery.

number = .......................................[3]

Calculate the resistance of X.

resistance = ........................................ Ω [1]

(iv)

Use your answer in (b)(iii) to determine the ratio

 

ratio = .................................. [2]

State and explain the effect, if any, of this temperature change on the total power produced by the battery.

[3]

Explain why the terminal potential difference (p.d) of a cell with internal resistance may differ from the electromotive force (e.m.f) of the cell.

A battery of e.m.f 6.2 V and internal resistance 7.0 Ω is connected in series with a resistor of resistance 11 Ω as shown in Fig 1.1.

The current  flows through the circuit

(i)

the current in the circuit,

[3]

 

(ii)

the terminal p.d. of the battery.

[2]

A second identical resistor is added in series with the resistor in Fig 1.1. 

Quantitatively explain the change in the current in the circuit.

The second 11 Ω resistor is now connected in parallel to the initial 11 Ω resistor in Fig 1.1. 

Qualitatively explain the effect this has on the battery. 

A student investigates the potential difference in a circuit. The circuit is set up as shown in Fig. 2.1.

Fig. 2.1

Two resistors P and Q are connected in series to a power supply of electromotive force (e.m.f.) E and negligible internal resistance. Resistor P has resistance P.

The potential difference V across resistor P is measured. The experiment is repeated for different values of P.

It is suggested that V and P are related by the equation

where Q is the resistance of resistor Q. The value of Q is kept constant.

A graph is plotted of on the y-axis against on the x-axis.

Determine expressions for the gradient and the y-intercept.

Values of P, V and are given in Table 2.1.

Table 2.1

P / Ω	V / V	/ 10–3 Ω–1	/ V–1
250	0.66		1.52
330	0.86		1.16
470	1.15		0.870
560	1.30		0.769
680	1.49		0.671
840	1.64		0.610

 
Each value of P has an uncertainty of ±10%.

Calculate and record values of / 10^–3 Ω^–1 in Table 2.1.

Include the absolute uncertainties in .

(i)

Plot a graph of / V^–1 against / 10^–3 Ω^–1.

Include error bars for .

[2]

[2]

gradient = ......................................... [2]

y-intercept = ......................................... [2]

E = ..............................................
Q = .............................................
[2]

percentage uncertainty in E = ......................................... % [1]

absolute uncertainty in Q = ........................................ [1]