Kirchhoff's laws

A 1.0 k resistor is connected in series to a battery made of three 1.2 V cells connected as shown. The cells have negligible internal resistance.

What is the reading on the ammeter?

A 1.2 mA

B 1.8 mA

C 2.4 mA

D 3.6 mA

Your answer

The circuit diagram of an electrical circuit is shown below.

The positive terminals of the batteries are connected together. One battery has electromotive force (e.m.f.) 4.5 V and internal resistance 0.80 . The other battery has e.m.f. 2.4 V and internal resistance 0.50 . R is a coil of insulated wire of resistance 1.2 at room temperature.

The switch S is closed.

On the diagram, draw an arrow to show the direction of the conventional current.

Calculate the current I shown by the ammeter.

The current measured by the ammeter is smaller than that calculated in (ii). This is because the temperature of R increased due to heating by the current.

Without any changes to the circuit itself, state and explain what practically can be done to make the measured current the same as the calculated current..

A light-emitting diode (LED) emits red light when it is positively biased and has a potential difference (p.d.) greater than about 1.8 V.

The energy of a photon of red light is about 1.8 eV.

Calculate the wavelength of this red light.

The LED is connected into a circuit, as shown below.

The battery has electromotive force (e.m.f.) 4.5 V and negligible internal resistance. The resistor R has resistance 150 . Assume the p.d. across the LED is 1.8 V.

The diagram below shows a circuit designed by a student.

The LED is very close to, and facing the light dependent resistor (LDR). The circuit is taken into a dark room.

The student thought that the LED would switch on. Instead, the LED was found to repeatedly switch on and off.

Explain this behaviour of the LED in this potential divider circuit.

Suggest a possible refinement so that the LED switches on permanently when taken into the dark room.

Which law indicates that charge is conserved?

A Lenz’s law

B Coulomb’s law

C Kirchhoff’s first law

D Faraday’s law of electromagnetic induction

Your answer

State Kirchhoff’s second law and the physical quantity that is conserved according to this law.

On Fig. 18.2 draw the straight line of best fit. Determine the gradient of this line.

gradient =........ A^–1 m^–1

Show that the gradient of the line is , where is the resistivity of the material of the wire, A is the area of cross-section of the wire and E is the e.m.f. of the cell.

The e.m.f. E of the cell is 1.5 V. The diameter of the wire is 0.38 mm.

Use your answer to (i) and the equation given in (ii) to determine .

=........ m

Fig. 18.1 shows a circuit.

The cell has e.m.f. 1.5 V. The cell and the variable power supply both have negligible internal resistance.

The e.m.f. of the power supply is set at 4.2 V. Calculate the current I in the 33 resistor.

The e.m.f. of the variable supply is now slowly decreased from 4.2 V to 0 V. Describe the effect on the current I in the 33 resistor.

* A group of students are investigating the power dissipated in a variable resistor connected across the terminals of a cell. The cell has e.m.f. 1.5 V. The students determine the power P dissipated in the variable resistor of resistance R.

Fig. 18.2 shows the data points plotted by the students on a graph of P (y-axis) against R (x-axis).

The group of students know that maximum power is dissipated in the variable resistor when R is equal to the internal resistance r of the cell.

Describe, with the help of a suitable circuit diagram, how the students may have determined P and R. Use Fig. 18.2 to estimate the internal resistance r of the cell and discuss any limitations of the data plotted by the group.