Series and parallel circuits

*3 A student connects three identical 3 V bulbs to a 6 V battery of negligible internal resistance. The circuit includes two switches, S₁ and S₂, as shown.

The student closes S₁ and records the brightness of each bulb.

With S₁ still closed, the student closes S₂.

Explain how the brightness of bulb 1 compares with the brightness of bulb 2 before and after S₂ is closed.

A battery has an e.m.f. of 12 V and an internal resistance of 0.50 Ω. The battery is connected into a circuit, as shown.

Each bulb has a normal working power of 40 W when a potential difference (p.d.) of 12 V is applied.

Initially the switch is open.

Calculate the terminal p.d. of the battery when bulb 1 is lit. Assume that the resistance of the bulb has its normal working value.

Terminal p.d. of battery =_........

Explain how the brightness of bulb 1 changes when the switch is closed. No further calculations are necessary.

A student is planning to collect data to produce a current-potential difference graph for a filament lamp. Her teacher suggests two circuits that she could use.

Circuit 1 uses a potential divider and circuit 2 uses a variable resistor to vary the potential difference across the filament lamp.

*(a) Discuss the suitability of each circuit to collect the data.

The student sets up the following circuit with the filament lamp. The battery has negligible internal resistance.

The reading on the ammeter is 17.5 mA. Calculate the value of the potential difference (p.d.) across the filament lamp.

p.d. across filament lamp =_........

When a voltmeter with a resistance of 1.5 kΩ is connected as shown, the p.d. across the filament lamp decreases.

Explain why the p.d. across the filament lamp decreases.

Questions 4 and 5 refer to the information below.

Two resistors are connected in parallel and the current in one of them is 2.0 A, as shown.

5 Which of the following is the total resistance of the resistors in parallel?

The diagrams show the plan view and side view of a moving coil ammeter.

The fixed soft iron cylinder and magnets produce a uniform magnetic field of magnetic flux density B. The coil is able to rotate within this magnetic field. The coil has width w and length l. There is a current I in the coil in the direction shown in the side view diagram.

Explain which way the coil will rotate.

Show that the moment M on the coil about the pivot, due to the magnetic field, is given by

M = BAIN

where A is the cross-sectional area of the coil N is the number of turns of wire on the coil.

An ammeter of this type has a resistance of 625 Ω and will measure a maximum current of 1.6 mA.

The ammeter can be adapted to measure potential difference by adding a resistor in series with the ammeter. This resistor is known as a multiplier.

The ammeter is adapted so that it can measure potential differences up to 5.0 V as shown.

The following multipliers are available:

200 Ω 2500 Ω 3125 Ω 3750 Ω

Deduce which multiplier should be used.

The coil within a very sensitive moving coil ammeter can be damaged when the ammeter is transported. The two ends of the coil are connected together when the ammeter is transported. This reduces the movement of the coil and makes it less likely to be damaged.

A student suggests that this is due to Faraday’s law and Lenz’s law.

Explain how these laws apply to this situation.

A student is experimenting with different combinations of springs and recalls that in physics it is often possible to model different physical situations in similar ways.

The student suggests that a parallel combination of springs could be a model for a parallel combination of resistors in a circuit.

Derive an expression for the effective resistance R_eff of two resistors R₁ and R₂ connected in parallel in a circuit.

Assess the validity of the student’s suggestion by considering the effective stiffness of two identical springs in parallel.