A heating element has a resistance of 900 ohms. If a current of 0.3 A flows through it for 10 seconds, how much heat energy is generated in the element in joules?

Introduction / Context:

This numerical physics question applies Joule heating or Joule law of electric heating. When an electric current flows through a resistor, electrical energy is converted into heat energy. Calculating the heat generated is important for the design of heaters, fuses, and electrical appliances to ensure efficiency and safety.

Given Data / Assumptions:

• Resistance of the heating element, R = 900 ohms.
• Current flowing through the element, I = 0.3 A.
• Time for which current flows, t = 10 seconds.
• We assume constant current and resistance during the interval.
• We want heat energy in joules.

Concept / Approach:

According to Joule law of heating, the heat energy H produced in a resistor when current flows is given by H = I^2 * R * t, where I is current, R is resistance, and t is time. In SI units, if I is in amperes, R in ohms, and t in seconds, then H is in joules. The calculation involves squaring the current, multiplying by resistance, and then by time. Careful arithmetic and attention to units yield the correct answer.

Step-by-Step Solution:

Verification / Alternative check:

As a rough check, note that 0.3 A is less than 1 A, so heat generated will be less than 900 * 10 = 9000 J, since that would correspond to 1 A. More precisely, I^2 is 0.09, less than one tenth, so we expect around 0.09 times 9000 J, which is about 810 J. This estimate matches the exact computation. Also, unit analysis confirms that amperes squared times ohms times seconds yields joules, as required.

Why Other Options Are Wrong:

• 2700 J: Could result from using I instead of I^2 or a different mistaken combination in the formula.
• 405 J: This is half of the correct value and may arise from using half the correct time or resistance by mistake.
• 1350 J: This value does not follow from the correct substitution and may come from calculating 0.3 * 900 * 5 instead of using I^2 and full time.

Common Pitfalls:

Students sometimes confuse the formulas H = I^2 * R * t, H = V * I * t, and H = V^2 * t / R. While all are equivalent, using the wrong one without proper substitution leads to errors. Another frequent mistake is forgetting to square the current in H = I^2 * R * t. Misplacing decimal points when squaring 0.3 or multiplying also causes incorrect answers. To avoid these, write each step clearly, check powers carefully, and perform a quick magnitude estimate to see if the result is reasonable.

Final Answer:

The heat generated in the element is 810 J.