(a) Given: V = 220 V
At maximum rate (P = 880 W):
$$I = \frac{P}{V} = \frac{880}{220} = 4 \text{ A}$$
$$R = \frac{V}{I} = \frac{220}{4} = 55 \text{ Ω}$$
At minimum rate (P = 330 W):
$$I = \frac{P}{V} = \frac{330}{220} = 1.5 \text{ A}$$
$$R = \frac{V}{I} = \frac{220}{1.5} = 146.67 \text{ Ω}$$
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(b) When electric current flows through a conductor, the moving electrons collide with atoms, and electrical energy is converted into heat energy. This is called the heating effect of electric current (Joule's heating effect).
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(c) Consider a resistor of resistance R. Current I flows through it for time t. The charge that flows is Q = It.
Work done (electrical energy supplied):
$$W = VQ = V \cdot It$$
By Ohm's law, V = IR, so:
$$H = I^2 R t$$
This is Joule's Law of Heating — heat produced is directly proportional to I², R, and t.
Source: Chapter 11 – Electricity, Section 11.7
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