Determine the maximum current passing through a 2.7-hp pump connected to a 240-V_rms ac power source.

Verified step by step guidance

1. Identify the relevant physical principles: To determine the maximum current passing through the pump, we need to use Ohm's Law, which relates voltage (V), current (I), and resistance (R) as \( I = \frac{V}{R} \). Additionally, if the pump is powered by an alternating current (AC) source, we may need to consider the root mean square (RMS) values of voltage and current.
2. Gather the given data: Look for the values of the voltage supplied to the pump and the resistance of the pump's circuit. If the problem involves AC, ensure you are using the peak voltage (\( V_{\text{peak}} \)) to calculate the maximum current.
3. Convert RMS voltage to peak voltage if necessary: If the voltage provided is the RMS value, convert it to the peak value using the formula \( V_{\text{peak}} = V_{\text{RMS}} \times \sqrt{2} \). This step is crucial for calculating the maximum current in an AC circuit.
4. Apply Ohm's Law: Substitute the peak voltage (\( V_{\text{peak}} \)) and the resistance (R) into the formula \( I = \frac{V}{R} \) to calculate the maximum current.
5. Verify the units and interpret the result: Ensure that the voltage is in volts (V), resistance is in ohms (Ω), and the resulting current is in amperes (A). This will give you the maximum current passing through the pump.

Key Concepts

Current

Current is the flow of electric charge in a circuit, measured in amperes (A). It represents the rate at which charge is transferred through a conductor. Understanding current is essential for analyzing electrical systems, as it directly affects the performance and efficiency of devices like pumps.

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. This relationship is expressed as I = V/R, which is crucial for determining the maximum current in electrical circuits, including those involving pumps.

Power Rating

The power rating of a pump indicates the maximum electrical power it can handle, typically measured in watts (W). This rating is important for calculating the maximum current, as power (P) is related to current and voltage by the formula P = IV. Knowing the power rating helps ensure that the pump operates safely within its limits.