Heating Effect of Current: The electric energy consumed in a circuit is defined as the total work done in maintaining the current in an electric circuit for a given time.
Electric energy $=V I t=P t=I^{2} R t=V^{2} t / R$
The S.I. unit of electric energy is joule (denoted by J) where 1 joule $=1$ watt $\times 1$ second $=1$ volt $\times 1$ ampere $\times 1 \mathrm{sec}$. In household circuits the electrical appliances are connected in parallel and the electrical energy consumed is measured in $\mathrm{kWh}$
1.An electric fan and a heater are marked as $100 \mathrm{~W}, 220 \mathrm{~V}$ and $1000 \mathrm{~W}, 220 \mathrm{~V}$ respectively. The resistance of heater is
(a) equal to that of fan
(b) lesser than that of fan
(c) greater than that of fan
(d) zero
2.Which of the following statement is false?
(a) Some of the energy produced by the light bulb takes the form of heat.
(b) The battery is the source of all the electrons flowing around the circuit.
(c) The current entering the light bulb equals the current leaving the light bulb.
(d) The potential in the wire to the left of the light bulb differs from the potential in the wire to the right of that bulb.
3.Resistance of conductor is doubled keeping the potential difference across it constant. The rate of generation of heat will
(a) become one fourth
(b) be halved
(c) be doubled
(d) become four times
4.The heating element of an electric heater should be made with a material, which should have
(a) high specific resistance and high melting point
(b) high specific resistance and low melting point
(c) low specific resistance and low melting point
(d) low specific resistance and high melting point
5.If $R_{1}$ and $R_{2}$ are respectively the filament resistances of a 200 watt bulb and a 100 watt bulb designed to operate on the same voltage
(a) $\mathrm{R}_{1}$ is two times $\mathrm{R}_{2}$
(b) $\mathrm{R}_{2}$ is two times $\mathrm{R}_{1}$
(c) $\mathrm{R}_{2}$ is four times $\mathrm{R}_{1}$
(d) $\mathrm{R}_{1}$ is four times $\mathrm{R}_{2}$
a)b,b,c,a,b b)b,c,b,a,b c)b,b,b,a,b d)b,b,b,a,d
(b) As $\mathrm{R} \propto \mathrm{V}^{2} / \mathrm{P}$ or $\mathrm{R} \propto 1 / \mathrm{P}$, so resistance of heater is less than that of fan.
(b) Most of the charges flowing around the circuit are valence electrons stripped off the metal atoms in the wires and light bulbs. A battery doesn't "supply" all of the charges. It merely pushes around charges already present in the circuit.
Statements (c) and (d) are both true. All charges flowing into the light bulb also flow back out; no current gets " used up" But inside the bulb, those charges lose energy. This lost electrical energy converts into light and heat. So, the current has lower "potential" after flowing through the bulb.
(b) The rate of generation of heat, for a given potential difference is, $\mathrm{P}=\mathrm{V}^{2} / \mathrm{R}$
(a) A heating wire should be such that it produces more heat when current is passed through it and also does not melt. It will be so if it has high specific resistance and high melting point.
(b) $\mathrm{R}_{1}=\frac{\mathrm{V}^{2}}{\mathrm{P}_{1}}$ and $\mathrm{R}_{2}=\frac{\mathrm{V}^{2}}{\mathrm{P}_{2}}$
$\therefore \quad \frac{\mathrm{R}_{2}}{\mathrm{R}_{1}}=\frac{\mathrm{p}_{1}}{\mathrm{P}_{2}}=\frac{200}{100}=2(\because \mathrm{V}=\mathrm{constant})$
$\mathrm{R}_{2}=2 \mathrm{R}_{1}$
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