Final answer:
The heat produced in a 100 cm resistance wire with a resistance per unit length of 0.02 ohm·cm and a voltage of 15 volts applied across it for 1 minute is 6750 joules.
Step-by-step explanation:
To calculate the heat produced in a resistance wire when a voltage is applied, we can use Joule's law of heating, which states that the heat (H) produced in a resistor is directly proportional to the square of the current (I), the resistance (R), and the time (t) for which the current flows through the resistor. The formula is given by H = I^2 · R · t. First, we need to find the total resistance of the wire. Since the resistance per unit length is 0.02 ohm·cm and the length of the wire is 100 cm, the total resistance R is 2 ohms. Using Ohm's law, V = I · R, we can calculate the current I by rearranging the formula to I = V / R. With V being 15 volts, the current I is 7.5 A. Therefore, the heat produced in one minute (60 seconds) is H = (7.5 A)^2 · 2 ohms · 60 s, which equals 6750 joules of heat.