Electric Heating and How Electricity Consumption is Measured

Understanding

• All heating elements → high electrical resistances.
• These resistances oppose the flow of charge. In the case of alloys → free electrons bump into ions → which are obstructions to the flow.
• As a result of the collision → fixed position ions vibrate more vigorously → which in turn raise temperature of the alloys
• Rise in temp → means that energy in internal store of elements increased. Energy in internal store is useful and hence we want to know how to measure this amount of energy.

Recall Current of Electricity Main Note $V=\frac{W}{Q}$

Since $Q=It$ → we can obtain WD in terms of voltage, current and time.

Formulae

$W=VIt$ where: V = p.d. of electrical component or heating element (V) I = current flowing through component A t = time(s) W is in joules #physicsFormulae

---

Very often → electrical appliances do not state electricity consumption. electricity consumption of electrical appliance → depends on its usage → is different for each household. Instead of stating electricity consumption → power rating is given.

---

Recall Energy → $P=\frac{W}{t}$ By replacing $W$ with $VIt$, and simplifying, we have:

Formulae

$P=VI$ P = power in W V = voltage I = Current

An important manipulation of the formula is $I=\frac{P}{V}$ #physicsFormulae

Definition

Power rating of appliance indicates the maximum allowable voltage and current for each appliance. Operating voltage is the voltage level which an electrical system is designed to operate at. #PhysicsDefinitions

In case of heating appliances → energy is transferred electrically to internal store of the resistor. To measure the rate at which energy is transferred to the internal store of the resistor → we can make use of this relationship, $V=IR$ → in our energy and power equations.

Since $W=VIt$ → its relationship to the resistance of the heating element is: $W=I^{2}Rt(sinceV=IR)$ $W=\frac{V^{2}t}{R}(sinceI=\frac{V}{R})$ I = current flowing in resistor or heating element (A) R = resistance of resistor or heating element ($\text{ohm}$) t = time (s) V = p.d. across the resistor or heating element (V)

Energy measured in joules (J) and is scalar quantity

Relationship between power and resistance of heating element is: $P=I^{2}R(sinceV=IR)$ $P=\frac{V^2}{R}(SinceI=\frac{V}{R})$ I = current flowing in the resistor or heating element (A) R = resistance of the resistor or heating element ($\text{ohm}$) V = p.d. across resistor or heating element (V)

Power measured in watt(W) and is also scalar quantity

Note

$P=I^{2}R$ → often used to find out power loss → due to resistance in wires or components. commonly referred to as power dissipated by heat

$P=\frac{V^2}{R}$ → often used to calculate power dissipated in resistor, power loss in transmission lines, heating effect in appliances or circuits

---

To conserve energy + reduce carbon footprint, it is important to:

• reduce usage of appliances with higher electricity consumption
• choose those with lower electricity consumption if possible

---

Amount of electricity consumed is measured in kilowatt hours(kW h)

• each kilowatt hour is equivalent to 3.6MJ → that is 3 600 000 joules of energy → measuring household electricity consumption in SI unit → impractical → number is very large and cumbersome to read.

1 kWh = 1kW $\times$ 1 h = 1000W $\times$ 3600s = $3.6\times 10^{6}J$

---

Extra***

1. some sections of wire have equal cross sectional area but different lengths. state relationship between power P lost in each of these sections and the length l of each section

• since resistance is proportional to length, and power loss is proportional to resistance, the power loss is proportional to length

1. other sections have equal lengths but different cross sectional areas. state relationship between power P lost in each of these sections and the cross sectional area A of the section.

• since resistance is inversely proportional to cross sectional area, and power loss is proportional to resistance, power loss is inversely proportional to the cross sectional area.

---

Example

60W lamp means it uses 60J/s