Askiitians Tutor Team
Last Activity: 12 Days ago
To determine the power consumed by the water heater when the voltage drops from 220V to 180V, we can analyze both methods you've presented. Let's break down each approach step by step to see which one is correct and why.
Understanding the Basics of Power Calculation
Power in electrical systems can be calculated using the formula:
- P = V × I, where P is power, V is voltage, and I is current.
From the specifications of the heater, we know:
- Rated Power (P1) = 1500W
- Rated Voltage (V1) = 220V
Method 1: Using Current Calculation
In the first method, you calculated the current (I) at the rated voltage:
- P1 = V1 × I
- 1500 = 220 × I
- I = 1500 / 220 = 6.818 A (approximately)
Now, using this current to find the new power (P2) at the reduced voltage (V2 = 180V):
- P2 = V2 × I
- P2 = 180 × 6.818 = 1227.27 W (approximately)
Method 2: Using Resistance Calculation
The second method involves calculating resistance (R) from the rated power and voltage:
- P1 = V1² / R
- R = V1² / P1 = (220²) / 1500 = 32.4 ohms (approximately)
Then, using this resistance to find the new power at the lower voltage:
- P2 = V2² / R
- P2 = (180²) / 32.4 = 1004.13 W (approximately)
Comparing the Methods
Both methods are valid, but they yield different results due to the assumptions made in each calculation. Let's analyze:
- **Method 1** assumes that the current remains constant when the voltage drops, which is not true for resistive loads like heaters. As voltage decreases, the current also decreases, leading to a lower power consumption.
- **Method 2** correctly accounts for the change in resistance and how it affects power when voltage changes. This method reflects the actual behavior of the heater under different voltage conditions.
Conclusion on Correctness
Given that the heater is a resistive load, the second method is more accurate. The power consumed at 180V is approximately 1004.13W, as calculated using the resistance derived from the rated conditions. This aligns with the principles of Ohm's Law and the behavior of resistive circuits.
Final Thoughts
In practical applications, it's essential to consider how devices respond to changes in voltage. For resistive loads, power consumption will decrease with lower voltage, as shown in Method 2. Understanding these principles helps in making informed decisions about electrical appliances and their efficiency.
