Water is heated with a coil of resistance R connected to domestic supply. The rise of temperature of water will depend on 1) Supply voltage 2) Current passing through the coil. 3) Time for which voltage Is supplied
1, 2 and 3
Understanding Water Heating with a Resistance Coil
When water is heated using a coil of resistance connected to a domestic supply, electrical energy is converted into heat energy. This phenomenon is known as Joule heating or the heating effect of electric current. The heat generated by the resistance coil is then transferred to the water, causing its temperature to rise.
Factors Affecting Heat Generation
The amount of heat (\(H\)) generated by a resistance coil when an electric current flows through it depends on several factors. According to Joule's law of heating, the heat generated can be calculated using the following formulas:
- If the current (\(I\)) and resistance (\(R\)) are known, and the current flows for time (\(t\)): $$H = I^2 R t$$
- If the voltage (\(V\)) across the resistance and the current (\(I\)) are known, and the current flows for time (\(t\)): $$H = V I t$$
- If the voltage (\(V\)) across the resistance and the resistance (\(R\)) are known, and the voltage is applied for time (\(t\)): $$H = \frac{V^2}{R} t$$
From these formulas, it is clear that the heat generated is directly proportional to the square of the current, the resistance of the coil, the applied voltage, and the time for which the current flows.
Relationship between Heat and Temperature Rise
The rise in temperature (\(\Delta T\)) of a substance, like water, when heat energy (\(H\)) is added to it depends on the mass of the substance (\(m\)) and its specific heat capacity (\(c\)). The relationship is given by the formula:
$$H = m c \Delta T$$Rearranging this formula, we can see that the temperature rise is directly proportional to the heat added and inversely proportional to the mass and specific heat capacity:
$$\Delta T = \frac{H}{m c}$$Assuming the mass of the water and its specific heat capacity are constant during the heating process, the rise in temperature of the water will be directly proportional to the amount of heat energy absorbed from the coil.
Analyzing the Factors from the Question
Let's examine how each factor mentioned in the question affects the rise in temperature of the water.
1) Supply Voltage
The supply voltage (\(V\)) is directly related to the heat generated, as shown by the formula \(H = \frac{V^2}{R} t\). If the supply voltage increases, the heat generated increases (assuming resistance and time are constant). An increase in heat generated leads to a higher rise in water temperature (\(\Delta T \propto H\)). Therefore, supply voltage affects the rise of temperature of water.
2) Current Passing Through the Coil
The current (\(I\)) passing through the coil is also directly related to the heat generated, as shown by the formula \(H = I^2 R t\). If the current increases, the heat generated increases (assuming resistance and time are constant). More heat means a greater rise in water temperature (\(\Delta T \propto H\)). Therefore, the current passing through the coil affects the rise of temperature of water.
3) Time for Which Voltage Is Supplied
The time (\(t\)) for which the voltage is supplied (and thus current flows) is directly proportional to the heat generated, as shown by all formulas (\(H = I^2 R t\), \(H = V I t\), \(H = \frac{V^2}{R} t\)). If the time increases, the heat generated increases (assuming voltage/current and resistance are constant). More heat transferred to the water over a longer period results in a higher rise in water temperature (\(\Delta T \propto H\)). Therefore, the time for which voltage is supplied affects the rise of temperature of water.
Conclusion
Based on the analysis of Joule heating and the relationship between heat and temperature rise, all three factors listed in the question – supply voltage, current passing through the coil, and the time for which voltage is supplied – directly influence the amount of heat generated by the resistance coil and subsequently the rise in temperature of the water.
| Factor | Effect on Heat Generated (H) | Effect on Temperature Rise (\(\Delta T\)) |
|---|---|---|
| Supply Voltage (V) | \(H \propto V^2\) | \(\Delta T \propto V^2\) |
| Current (I) | \(H \propto I^2\) | \(\Delta T \propto I^2\) |
| Time (t) | \(H \propto t\) | \(\Delta T \propto t\) |
Thus, the rise of temperature of water will depend on all three factors: supply voltage, current passing through the coil, and the time for which voltage is supplied.
Revision Table: Water Heating Factors
| Concept | Description | Key Formulas |
|---|---|---|
| Joule Heating | Conversion of electrical energy into heat energy in a resistor. | \(H = I^2 R t\), \(H = V I t\), \(H = V^2/R \cdot t\) |
| Temperature Rise | Increase in temperature due to heat absorption. | \(\Delta T = H / (m c)\) |
| Dependence on V | Higher voltage means more heat and higher \(\Delta T\). | \(\Delta T \propto V^2\) |
| Dependence on I | Higher current means more heat and higher \(\Delta T\). | \(\Delta T \propto I^2\) |
| Dependence on t | Longer heating time means more heat and higher \(\Delta T\). | \(\Delta T \propto t\) |
Additional Information: Related Concepts
- Electric Power: The rate at which electrical energy is converted to heat is power (\(P\)). \(P = V I = I^2 R = \frac{V^2}{R}\). Heat generated \(H = P \times t\). This shows that heat depends on power and time. Power itself depends on voltage, current, and resistance.
- Resistance (R): The resistance of the coil also affects the heat generated (\(H \propto R\) for constant current, \(H \propto 1/R\) for constant voltage). While not listed as a variable factor in the options, the specific resistance of the coil is a constant property that influences the heating rate for given voltage or current.
- Specific Heat Capacity (c): This is a property of the substance being heated (water). It represents the amount of heat energy required to raise the temperature of 1 unit mass of the substance by 1 degree. Water has a relatively high specific heat capacity.
- Mass of Water (m): The amount of water being heated. More water requires more heat energy to achieve the same temperature rise (\(H \propto m \Delta T\)).
Similar Questions
An electric bulb is connected to 220 V generator. The current drawn is 600 mA. What is the power of the bulb?
Two metallic wires A and B are made using copper. The radius of wire A is r while its length is l. A dc voltage V is applied across the wire A, causing power dissipation, P. The radius of wire B is 2r and its length is 2l and the same dc voltage V is applied across it causing power disspation P 1. Which one of the following is the correct relationship between P and P 1?
Which one of the following formulas does not represent electrical power?
- What is the current required to light a 60 W incandescent bulb in a domestic supply of 240 V ?
One-kilowatt hour is equal to
In an electric circuit, a wire of resistance 10 Ω is used. If this wire is stretched to a length double of its original value, the current in the circuit would become :
Which one of the following terms cannot represent electrical power in a circuit?
An electric bulb is rated as 220 V and 80 W. When it is operated on 110 V, the power rating would be:
Important Questions from Power in Electric Circuits
Two electric bulbs marked 25 W - 220 V and 100 W - 220 V are connected in series with 440 V supply. Which of the bulb will fuse?
Two heaters are marked 200V,300W & 200V,600W. If the heaters are connected in series and the combination connected in series and the combination connected to a 200 V dc supply, then which option is true out of the following?
- Two electric bulbs are rated '$220$ V, $100$ W' and '$220$ V, $50$ W' respectively.
If these two bulbs are connected in series across a $220$ V supply, what will be the power consumed by the $100$ W bulb? - Three identical bulbs are connected in parallel to a battery of 6 V. If the current in the circuit is 0.6 A, the power dissipated by the battery is:
- A bulb is connected across a battery of 10 V for 20 seconds. If a current of 2 A flows through it, calculate the heat energy generated by the bulb.
