Given below are two statements : Statement I : If a copper and a nichrome wire of same length and same area of cross-section carry the same current for same time at room temperature then both will produce the same amount of heat. Statement II : If current in a conductor is doubled and time is halved then the heat produced becomes double. In the light of the above statements, choose the correct answer from the options given below:

Joule's law of heating

• The heat produced in a resistor is given by H = I squared into R into t, that is, it is directly proportional to the square of the current, to the resistance and to the time for which the current flows.
• The resistance of a wire is R = rho into l upon A. For the same length and the same area of cross-section, the resistance depends on the resistivity of the material. The resistivity of nichrome is much higher than that of copper, so the nichrome wire will have a much greater resistance and will produce much more heat for the same current and time. Hence, statement I is false.
• This is why the coils of electric heaters and toasters are made of an alloy such as nichrome, while copper is used for connecting wires.
• If the current is doubled and the time is halved, the new heat produced is (2I) squared into R into (t upon 2), which equals 2 into I squared into R into t. The heat produced therefore becomes double. Hence, statement II is true.