A coffee cup immersion heater utilizes a heating coil with a resistance of 8.5 ohms. Determine the current through the coil when operated at 0.11 kV.
Understand the Problem
The question is asking to determine the current through a heating coil utilizing the resistance and voltage provided. The user is applying Ohm's Law (I = V/R) to solve the problem.
Answer
The current through the heating coil is approximately $I = 13 \, A$.
Answer for screen readers
The current through the heating coil is approximately ( I = 13 , A ).
Steps to Solve
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Identify Given Values We have the resistance $R = 8.5 , \Omega$ and the voltage $V = 0.11 , kV$.
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Convert Voltage to Volts Convert the voltage from kilovolts to volts: $$ V = 0.11 , kV \times 1000 = 110 , V $$
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Apply Ohm's Law Use Ohm's Law, which states $I = \frac{V}{R}$, to find the current: $$ I = \frac{110 , V}{8.5 , \Omega} $$
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Calculate the Current Perform the division: $$ I = \frac{110}{8.5} \approx 12.94 , A $$
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Round the Result Round the current to a reasonable number of significant figures: $$ I \approx 13 , A $$
The current through the heating coil is approximately ( I = 13 , A ).
More Information
This problem effectively utilizes Ohm's Law to find the current through an electrical component. Ohm's Law is fundamental in electrical engineering and physics, showing the relationship between voltage, current, and resistance.
Tips
- Incorrect Unit Conversion: It's important to convert kilovolts (kV) to volts (V) correctly to avoid calculation errors.
- Significant Figures: Rounding errors can happen if the result is not rounded appropriately according to the significant figures based on the given data.
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