This problem involves understanding the relationship between potential difference, current, and resistance in an electric circuit, as described by Ohm's Law. An electric heater behaves as a resistor. Assuming its resistance remains constant, we can use the initial conditions to find its resistance and then use that resistance to find the current at a different potential difference.

Analyzing the Electric Heater Problem

We are given the following information for an electric heater:

• Initial potential difference, \(V_1 = 220\) V
• Initial current, \(I_1 = 0.5\) A
• New potential difference, \(V_2 = 120\) V

We need to find the new current, \(I_2\), through the heater when the potential difference is \(V_2\).

Applying Ohm's Law to Determine Heater Resistance

Ohm's Law states that the potential difference (\(V\)) across a conductor is directly proportional to the current (\(I\)) flowing through it, provided the temperature and other physical conditions remain unchanged. The constant of proportionality is the resistance (\(R\)) of the conductor. Mathematically, Ohm's Law is expressed as:

\(V = I \times R\)

From this formula, we can find the resistance using the initial values:

\(R = \frac{V_1}{I_1}\)

Let's calculate the resistance of the electric heater:

\(R = \frac{220 \text{ V}}{0.5 \text{ A}}\)

\(R = 440 \, \Omega\)

The resistance of the electric heater is \(440 \, \Omega\).

Calculating the New Current at Reduced Potential Difference

Now that we know the resistance of the heater (\(R = 440 \, \Omega\)) and the new potential difference (\(V_2 = 120\) V), we can use Ohm's Law again to find the new current (\(I_2\)).

\(V_2 = I_2 \times R\)

Rearranging the formula to solve for \(I_2\):

\(I_2 = \frac{V_2}{R}\)

Let's calculate the new current:

\(I_2 = \frac{120 \text{ V}}{440 \, \Omega}\)

\(I_2 = \frac{12}{44} \text{ A}\)

\(I_2 = \frac{3}{11} \text{ A}\)

Converting the fraction to a decimal:

\(I_2 \approx 0.2727...\) A

Rounding to two decimal places, the current is approximately 0.27 A.

Step-by-Step Solution Process

1. Identify the knowns: Initial potential difference (\(V_1\)), initial current (\(I_1\)), and new potential difference (\(V_2\)).
2. Use Ohm's Law (\(R = V/I\)) with \(V_1\) and \(I_1\) to calculate the resistance \(R\) of the heater.
3. Use Ohm's Law (\(I = V/R\)) with \(V_2\) and the calculated resistance \(R\) to find the new current \(I_2\).
4. Perform the calculations: \(R = 220 \text{ V} / 0.5 \text{ A} = 440 \, \Omega\). \(I_2 = 120 \text{ V} / 440 \, \Omega = 3/11 \text{ A} \approx 0.27 \text{ A}\).

Revision Table: Key Physics Formulas

Additional Information: Understanding Electric Resistance

Electric resistance is a measure of how much a material opposes the flow of electric current. It is analogous to friction in mechanical systems. Materials with low resistance, like metals (copper, silver, aluminum), are good conductors, allowing current to flow easily. Materials with high resistance, like rubber or glass, are insulators, which restrict current flow significantly.

The resistance of a conductor depends on several factors:

• Length: Resistance is directly proportional to the length of the conductor. Longer conductors have higher resistance.
• Cross-sectional Area: Resistance is inversely proportional to the cross-sectional area. Thicker conductors have lower resistance.
• Material: Different materials have different inherent resistances, characterized by their resistivity (\(\rho\)).
• Temperature: For most metallic conductors, resistance increases with increasing temperature.

The formula relating these factors is:

\(R = \frac{\rho L}{A}\)

where \(R\) is resistance, \(\rho\) is resistivity, \(L\) is length, and \(A\) is cross-sectional area. In the case of an electric heater element, the material, length, and area are fixed, so its resistance is constant under normal operating conditions, assuming temperature effects are negligible or accounted for within the context of the problem.