Exam practice

A solar panel gives d.c. at a low voltage, but a ceiling fan has an a.c. motor made for about 230 V. Its motor needs a current that keeps reversing to keep turning, and a steady d.c. can’t do that. To run it from a solar panel you need a battery and an inverter (or a fan made for d.c.).

An electric current produces a magnetic field around the wire (the magnetic effect of current). This field acts on the magnetic needle of the compass and turns it.

The bell needs a magnet that can be switched on and off quickly and repeatedly. An electromagnet attracts the iron arm and hammer only while current flows; when the arm moves, it breaks the circuit, the magnetism disappears, the arm springs back and closes the circuit again. This happens many times a second and makes the hammer strike the gong again and again. A permanent magnet could not be switched off.

The output voltage depends on the turns ratio: $V_s/V_p = N_s/N_p$. If the turns were equal, the output voltage would equal the input and the transformer would do nothing. To step the voltage up, the secondary has more turns; to step it down, fewer.

The changing magnetic field induces currents in the iron core itself (eddy currents), which heat the core and waste energy. Making the core from thin iron sheets insulated from each other breaks up these currents, so less heat is produced and less energy is lost.

The mains supply is about 230 V a.c., but a phone battery is charged at about 5 V. A step-down transformer in the charger lowers the voltage (a rectifier then turns it into d.c.). Connected straight to 230 V, the phone would be destroyed.

The alternating current completes 50 cycles every second. Each cycle takes 1/50 s = 0.02 s, and since the current reverses twice in each cycle, it changes direction 100 times every second.

See Figure 11.3. For d.c., draw a horizontal straight line above the time axis (the current stays the same, e.g. 4 A). For a.c., draw a smooth wave that rises from zero to a maximum (e.g. +5 A), falls through zero to the same size in the negative direction (−5 A), and returns to zero: one cycle. Label the axes current (A) and time (s).

For a straight wire: concentric circles around the wire, closer together near it, with arrows showing the direction given by the right-hand thumb rule (see Figure 11.7). For a solenoid: straight parallel lines inside, curving round outside from the north end to the south end like a bar magnet (see Figure 11.8).

• i.If a straight current-carrying wire is gripped in the right hand with the thumb pointing in the direction of the current, the curled fingers show the direction of the magnetic field lines around the wire.
• ii.If a solenoid is held in the right hand with the fingers curled in the direction of the current in its turns, the thumb points to the solenoid’s north pole.

The production of a magnetic field around a conductor when an electric current flows through it. The direction of the field depends on the direction of the current. It was discovered by Oersted in 1820.

Magnetic flux through a surface is the total number of magnetic lines of force passing through it. It measures how much magnetic field passes through an area. Its symbol is Φ and its SI unit is the weber (Wb).

Pass a straight thick wire vertically through the middle of a piece of cardboard held horizontally. Connect the wire to a cell (or two) and a switch. Sprinkle fine iron filings evenly on the cardboard. Switch the current on and tap the cardboard gently. The filings arrange themselves in concentric circles around the wire, showing that the magnetic field lines are circles centered on the wire. Switch off soon, as the circuit has no resistance and the wire heats up.

Draw the wire as a vertical line (or, seen from above, a dot in a circle), with several concentric circles around it, spaced more widely as they go outwards. Mark the current direction on the wire and arrows on the circles using the right-hand thumb rule: anticlockwise (seen from above) for a current going up. See Figure 11.7.

A solenoid is a long cylindrical coil of many turns of insulated wire. When a current flows through it, it behaves like a bar magnet. Draw the coil, with straight parallel field lines inside it and lines curving outside from one end (N) round to the other end (S), as in Figure 11.8.

1. To make electromagnets (with a soft iron core), used in electric bells, cranes and relays.
2. In loudspeakers and earphones, and in solenoid valves and door locks that are opened by switching on a current. (Also: in transformers, induction cooktops and MRI machines.)

Both show the motor effect: a current-carrying conductor in a magnetic field experiences a force and moves. (If, in the left figure, the wire were moved by hand and connected to a galvanometer instead of a cell, it would show electromagnetic induction: a moving wire cutting field lines has a voltage induced in it.)

The paper clips hold the coil and connect its ends to the terminals of the dry cell, so a current flows through the coil. The current makes the coil a small electromagnet, and it lies in the field of the permanent magnet below. The two fields interact (the motor effect), so a force acts on the coil and it turns. One end of the coil wire has its insulation scraped off only on one half, so the current flows only during half of each turn; during the other half, the coil coasts round on its momentum. In this way the push always acts in the same turning direction, and the coil keeps spinning.

The production of an e.m.f. (voltage) in a conductor when the magnetic flux linked with it changes, for example when a magnet moves in or out of a coil, or a coil turns in a magnetic field. If the circuit is closed, an induced current flows.

• i.The galvanometer needle moves a little to one side: a small current is induced, because the flux changes slowly.
• ii.The needle moves further to the same side: the flux changes faster, so a larger e.m.f. is induced.
• iii.The needle returns to zero: the flux doesn’t change, so nothing is induced.
• iv.The needle moves a large amount to the opposite side: the flux is decreasing quickly, so a large current flows in the opposite direction.

When there is relative motion between a conductor and a magnet, an e.m.f. is induced in the conductor, and its size is directly proportional to the rate of change of the magnetic flux linked with the conductor.

The dynamo’s magnet is turned by the tyre. The induced e.m.f. is proportional to the rate of change of flux, that is, to how fast the magnet spins, which depends on the bicycle’s speed. Riding fast, the magnet spins fast and the bulb is bright; slowing down, the e.m.f. falls and the bulb dims; when the cycle stops, the magnet stops, the flux no longer changes, no e.m.f. is induced and the bulb goes off. A dynamo has no battery to store energy.

Any two of:

• 1.increase the number of turns in the coil;
• 2.use a stronger magnet;
• 3.turn the magnet (or coil) faster;
• 4.wind the coil on a soft iron core.

1. Upper Tamakoshi Hydroelectric Project, Dolakha. Capacity 456 MW (six units of 76 MW), completed in 2021, the largest in Nepal. It is a run-of-river project: water from the Tamakoshi River is diverted at a dam into an 8 km headrace tunnel and falls about 820 m to an underground powerhouse. It produces a.c.; the voltage is stepped up and sent on a 220 kV line to the national grid.
2. Nuwakot (Devighat area) Solar Farm, Nuwakot. NEA’s first large grid-connected solar plant, with a capacity of 25 MW, connected to the grid in 2022. Solar panels produce d.c.; inverters turn it into a.c., and transformers step it up to join the grid. It makes electricity only in daylight, and most in the dry season, when the rivers are low: it complements hydropower nicely.

(Check the figures for your own report with the Nepal Electricity Authority’s annual report, which is free online; figures change every year.)

A transformer is a device that increases or decreases the voltage of alternating current. It has two coils of insulated wire (primary and secondary) wound on a laminated iron core, and works on the principle of mutual induction.

J (at the power station) is a step-up transformer: it raises the voltage so the electricity can be sent over long distances with little loss. K (near the consumer) is a step-down transformer: it lowers the voltage to the safe 230 V used at home. See Figure 11.24.

See Figure 11.27: draw the iron core as a rectangle, with the primary coil on one side and the secondary on the other; for step-up, draw more turns on the secondary; for step-down, fewer.
Uses of a step-up transformer:

• 1.at power stations, to raise the voltage for transmission;
• 2.in microwave ovens (about 2,000 V for the magnetron). Also in X-ray machines.

Uses of a step-down transformer:

• 1.in mobile and laptop chargers and adaptors;
• 2.at substations and on electric poles, to bring the voltage down to 230 V for homes. Also in door bells.

Nₚ = 550, Vₚ = 220 V, Vₛ = 20 V, Nₛ = ?
$$\frac{N_p}{N_s} = \frac{V_p}{V_s} \quad\Rightarrow\quad N_s = \frac{N_p \times V_s}{V_p} = \frac{550 \times 20}{220} = 50$$
The secondary has 50 turns.

Nₛ = 10 Nₚ, so Nₚ/Nₛ = 1/10. Vₚ = 220 V.
$$\frac{1}{10} = \frac{220}{V_s} \quad\Rightarrow\quad V_s = 2200\ \text{V}$$
The secondary voltage is 2,200 V (a step-up transformer).

Nₚ/Nₛ = 22/1, Vₚ = 220 V.
$$\frac{22}{1} = \frac{220}{V_s} \quad\Rightarrow\quad V_s = \frac{220}{22} = 10\ \text{V}$$
The output voltage is 10 V (a step-down transformer).