The potential difference between the terminals of an electric heater is 60 V when it draws a current of 4 A from the source. Assuming the resistance of the heater remains constant, what current will it draw if the potential difference is increased to 127.5 V?

Introduction / Context:
Many electrical appliances such as heaters can be treated as resistive loads over a certain operating range. For such devices, Ohm's law applies, and the current drawn depends on the applied voltage and the fixed resistance of the appliance. This question gives you the current at an initial voltage and asks for the new current when the voltage is increased, assuming the resistance does not change. It tests your ability to calculate resistance first and then apply Ohm's law again at the new voltage.

Given Data / Assumptions:

• Initial potential difference V1 = 60 V.
• Initial current I1 = 4 A.
• Heater resistance R is assumed constant.
• New potential difference V2 = 127.5 V.
• We are asked to find the new current I2 at V2.

Concept / Approach:
First, we use Ohm's law V = I * R with the initial data to find the resistance of the heater. The formula rearranged gives R = V / I. Once we know R, we treat it as constant and use Ohm's law again with the new voltage to solve for the new current I2 = V2 / R. This two step approach is standard when you are given one set of voltage current data and asked to predict current at another voltage for an ohmic device.

Step-by-Step Solution:
Step 1: Use Ohm's law with the initial values to find the resistance: R = V1 / I1.Step 2: Substitute V1 = 60 V and I1 = 4 A to get R = 60 / 4 = 15 ohm.Step 3: Assume the heater's resistance remains at R = 15 ohm when the voltage changes.Step 4: Apply Ohm's law with the new voltage: I2 = V2 / R.Step 5: Substitute V2 = 127.5 V and R = 15 ohm to get I2 = 127.5 / 15 = 8.5 A.

Verification / Alternative check:
We can verify the arithmetic by checking the division: 15 * 8 = 120 and 15 * 0.5 = 7.5, so 15 * 8.5 = 127.5, confirming that 127.5 / 15 is indeed 8.5. Also, since the voltage a little more than doubles from 60 V to 127.5 V, we expect the current to a little more than double as well, because current is directly proportional to voltage for a fixed resistance. The initial current was 4 A, and a little more than twice that is around 8 A, so 8.5 A is a reasonable and consistent value.

Why Other Options Are Wrong:
Option B, 24 A, would imply a resistance far smaller than 15 ohm and would not match the initial V I data. Option C, 10 A, would correspond to a resistance of 12.75 ohm at the new voltage, which contradicts the constant resistance assumption. Option D, 12 A, implies an even smaller resistance when combined with 127.5 V. Only option A, 8.5 A, is consistent with both the original and new conditions under the assumption of constant resistance.

Common Pitfalls:
Some students try to directly proportion the currents and voltages without first finding the resistance, which can lead to mistakes if they misinterpret the proportionality. Another pitfall is miscalculating the initial resistance or failing to keep it constant in the second step. Always remember the correct order: use the first set of data to determine resistance, then apply Ohm's law with the second voltage. Writing out the formulas and numerical values step by step, as shown, helps avoid arithmetic and conceptual errors in these types of questions.

Final Answer:
8.5 A