Kirchhoff’s Laws (CIE AS 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]

•   the total energy transferred by the battery

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

•   the number of electrons that pass through the battery.

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

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

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

[3]

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 .

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]

The circuit shown in Fig. 1.1 contains a battery with an e.m.f. E  and negligible internal resistance r connected to four resistors R₁, R₂, R₃  and R₄, each of resistance R. 

Fig. 1.1

The current in R₃  is 0.40 A and the potential difference across R₄ is 3.2 V. 

Determine the resistance R  of each of the fixed resistors. 

Determine the e.m.f. of the battery. 

A fifth resistor R₅  also with resistance R  is now added in parallel to R₂  and R₃. The current through R₃  remains at 0.40 A. 

Determine the total current in this circuit. Explain your answer. 

The battery in the circuit is now replaced by one with the same e.m.f. but internal resistance is not negligible. 

Explain whether this will change the total power produced by the battery. 

A circuit containing a junction P has two power supplies with e.m.f 6.0 V and 2.0 V and two resistors with resistance 30 Ω and 10 Ω is shown in Fig. 1.1.

Fig. 1.1

Draw on the diagram to label the currents in each branch of the circuit and obtain an expression for the current at P. 

Determine the values of the currents at P for the circuit in part a). 

A combination of identical resistors each with resistance R  has a total resistance of 250 Ω as shown in Fig. 1.2. 

Fig. 1.2

Show, without the use of a calculator, how to find the value of resistance of each resistor and hence determine the value of R.

A student wishes to determine the resistance for three different resistors. They connect the resistors in a ‘T’ arrangement and change the position of the power source and the voltmeter, as shown in Fig. 1.1, to obtain two sets of results, as shown in Table 1.1. The power supply in Circuit 1 causes a current of 0.50 A in one branch of a circuit. 

Fig. 1.1

Table 1.1

Calculate the resistance of resistors ,  and .  

You may assume the voltmeter has an infinitely high resistance.

There is current flowing from P to R in the resistor network shown. The potential differences across three of the resistors are 3.0 V, 6.0 V and 5.0 V as shown in Fig. 1.1. 

Fig. 1.1

Determine the potential difference across the other two resistors. 

The current through the branch QS is 3 A in Fig. 1.1.  The total combined resistance of the resistors in the outer loop of the circuit is r  Ω.  The resistance in the outer loop of the circuit is split according to the ratio of the magnitudes of the potential differences of the resistors in each side of the loop. 

Obtain an expression in terms of r for the total resistance of all the resistors in the circuit. 

Diagram 1.2 shows a circuit where V₁  is a battery of 0.5 V, V₂  a battery of 1 V and V₃  a battery of 2 V. Each resistor has a resistance of 0.25 Ω.

Fig. 1.1

Determine the value of each current at junction A.