Monday, 6 June 2011

Physics: Current electricity

Current electricity
Circuit diagrams show the components of a circuit.
Some electric components:
-Battery, electric cell, a.c./d.c. supply
-Ammeter, Voltmeter, Galvanometer
-Light bulb, resistance, motor, rheostat, variable resistor
-Push switch, switch, single pole-double throw(SPDT) switch
-Wire, fuse and earthing
(Please refer to this site for the symbols)
Notes for drawing circuit diagram: We should use straight lines; put the power supply along the side if possible (not the middle), separate the circuit by their own functions and label the voltage if needed.
There’s a current (electricity) to flow through a circuit only if:
1)       There exist a source of electricity (e.m.f.)
2)       Closed (completed) circuit
Electric current is due to the flow of electric charges. The current at a certain point is the amount of charge flow per unit time, i.e., I = Q/t. For positive charge, direction of I = direction of charge flow, while for negative charge, direction of I = opposite of direction of charge flow. In common circuit the charge carrier is electron so the electron flow is opposite to the current flow. We call the direction of I as the conventional current. Current has unit Ampere (A).
It’s the measurement of energy in unit of charge.
1)       Electromotive force (e.m.f., ε) is the amount of energy gained when a unit charge (1C) pass through the battery.
2)       Potential difference (p.d.) between 2 points is the energy released from the charge when a unit charge pass through the two points.
Mathematically, E(gain) = εQ for e.m.f. while E(loss) = VQ for p.d. Both e.m.f. and p.d. has unit
Volt (V). Note that the voltage along the same wire without passing through any electrical components is the same.
Resistance = p.d. across the conductor / current pass through the conductor, R = dV/dI.
When dV/dI is constant, i.e., V=IR (k=1 by defining R), we say that’s obeying Ohm’s law, and the conductor is ohmic. The unit of resistance is Ohm (Ω).
When two resistors are connected in series, by V = IR, we have Ve = IRe = IR1 + IR2, since the current is the same along the same series, we have Re = R1 + R2.
For parallel circuit, by I = V/R, Ie = I1 + I2 (the mains current is equal to the sum of the current in the branches), V/Re = V/R1 + V/R2, 1/Re = 1/R1 + 1/R2. (p.d. across the parallel circuit is the same)
For a conductor, the resistance is given by R = ρl/A, where ρ is the resistivity of the conductor (unit Ωm), l is the length and A is the cross-sectional area.
I-V curve (V at y-axis; I at x-axis)
When a conductor is ohmic it’s a straight line. For most of the metals, it’s ohmic in lower temperatures (low I), and it becomes much steeper when it’s in higher temperatures (high I). It’s not ohmic anymore. It’s because the electron collides with the metal ions more frequently, causing higher temperature, and it makes electron harder to pass through the conductor, hence higher resistance. This is called the heating effect of metal. Note that thermistor is a special device with metal where resistance falls as temperature increase.
1)       Ammeter/galvanometer (for very small currents) should be put in series with the electrical appliances to be measured because it’s measuring the current along the wire. Ideal ammeter has zero resistance. (That is, connecting in series gives zero p.d. across the ammeter).
2)       Voltmeter should be put in parallel across the two points where p.d. to be measured. Ideal voltmeter has infinitely large resistance so p.d. across voltmeter = 0, so p.d. across the electrical appliances can be accurately measured.
3)       Resistance can be measured by R = V/I (note that ammeter/voltmeter here is NOT ideal)

-          When RI is comparable with R, we should connect the voltmeter across the resistance only. If not, p.d. across ammeter is comparable with p.d. across the resistance and if we measure p.d. across ammeter and resistance we can’t get the accurate result.
-          When RV is comparable with R, we connect the voltmeter across the ammeter and the resistance; otherwise if we connect the voltmeter across the resistance only, current pass through the voltmeter is not negligible.
Internal resistance
When the battery is connected lonely with the voltmeter, the reading shows the e.m.f. of the cell; when a resistance is added, the voltmeter measures the p.d. across the resistance which is smaller than the e.m.f. because internal resistance exists. Voltage across the external resistances V is given by V = ε – Ir.
Electrical power
Consider E = QV, P = E/t = QV/t = VI. P = VI is the definition of electrical power. If it’s ohmic, then P = VI = I2R = V2/R. Energy given out = Pt = VIt or other forms if it’s ohmic.
For a electrical appliances, it gives the operating voltage (or the operating current) and the output power, assuming that being an ohmic appliances, we can calculate its resistance.
Domestic electricity
The current supplied by the power stations are in forms of alternating current (a.c.) where direction of current changes alternately. (v(t) = Vmaxsin(ωt), where ω depends on the frequency, more about a.c. will be discussed in Ch. 29) In HK the supply is 220V at 50Hz.

The electrical cable consists of 3 wires:
1)       Live (brown) wire: bottom-right hole in the socket, its voltages varies as v(t) = Vmaxsin(ωt)
2)       Neutral (blue) wire: bottom-left hole in the socket, it’s earthed in the power station, so its potential is zero.
3)       Earth (green and yellow) wire: top hole in the socket, it’s earthed so zero potential.
Safety devices
1)       Fuse is applied to prevent too large currents flow. It melts when too large current pass through it since it’s overheated. The fuse value is usually slightly higher than the rated current of the electrical appliance. For example, 5A fuse is used for a circuit of 4.5A.
2)       Circuit breaker is a reusable type of fuse, operated by electromagnet.
3)       Switch is connected to the live wire to ensure the whole circuit is at zero potential when the switch is open.
4)       Electrical appliance with the sign means that it’s double insulated, where the appliances is enclosed in insulator casing so there’s no need make a earth-pin. The earth pins of these appliances are made of plastic.
5)       Earthing of appliances: the current flows from live, to the resistor and to the neutral wire. Without earthing, human have lower resistance than the resistor, so the current flows to the human, then to the Earth. This causes electric shock (100mA is fatal for human, domestic appliances have rated current several hundreds mA). The current flows to the earth wire due to much lower resistance if it exist.
Domestic circuit
1)       It passes through a consumer unit (the box of fuses) to control the electric supply, then it divides into lighting circuit, ring circuit and other individual appliances.
2)       Lighting circuit: The light bulbs and switches are connected in parallel

3)       Ring circuit: This circuit connects to the sockets.

4)       Some appliances like air conditioners are connected individually since it draws a large current, if they’re connected with the ring circuit, there’ll be a large energy dissipated in wire. Thick wire should be used.
The advantage of using lighting and ring circuit is that even one of the wire or appliances are broken, the others can still work. Also, in ring circuit, the current are divided into half, by P = I2R, the energy dissipated by the wire is reduced as well.

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