A 120 V power supply is connected to a resistor, and the current measured through it is 15 A. What is the resistance of the resistor, and how much power is dissipated?
["Understanding Power Dissipation in a Resistor: A 120 V Power Supply Connected to a High-Current Resistor", "When a power supply delivers electricity to a resistor, the relationship between voltage, current, resistance, and power is governed by fundamental electrical principles. One common scenario involves connecting a 120 V DC power supply directly across a resistor, resulting in a measurable current of 15 amps. This article explains how to calculate the resistor’s resistance and the power dissipated in the circuit—critical calculations for engineers, hobbyists, and students alike.", "### Step 1: Calculate the Resistance Using Ohm’s Law", "Ohm’s Law states:\n[ V = I \ imes R ]\nWhere:\n- ( V ) = Voltage (volts)\n- ( I ) = Current (amperes)\n- ( R ) = Resistance (ohms)", "Rearranging to solve for resistance:\n[ R = \frac{V}{I} ]", "Substitute the given values:\n( V = 120 ) volts,\n( I = 15 ) amps.", "[\nR = \frac{120}{15} = 8 , \Omega\n]", "So, the resistance of the resistor is 8 ohms.", "---", "### Step 2: Calculate the Power Dissipated", "Power dissipated in a resistor can be calculated using several equivalent formulas. One efficient and commonly used formula is:\n[ P = V \ imes I ]", "[\nP = 120 , \ ext{V} \ imes 15 , \ ext{A} = 1800 , \ ext{W}\n]", "Alternatively, using ( P = I^2 \ imes R ) or ( P = \frac{V^2}{R} ) yields the same result:", "[\nP = \frac{120^2}{8} = \frac{14400}{8} = 1800 , \ ext{W}\n]", "or", "[\nP = 15^2 \ imes 8 = 225 \ imes 8 = 1800 , \ ext{W}\n]", "Thus, the power dissipated across the resistor is 1,800 watts—a substantial amount requiring proper heat management.", "---", "### Why This Matters: Handling High Power", "Dissipating 1,800 W in a resistor means significant energy is converted into heat. This necessitates:", "- Heat sinks or active cooling to prevent damage.\n- Resistors rated for at least 2,000 watts (or higher margin) to handle continuous or peak loads.\n- Careful circuit design to avoid thermal runaway and ensure reliability.", "---", "### Summary", "| Parameter | Value |\n|------------------------|---------------|\n| Voltage (V) | 120 V |\n| Current (I) | 15 A |\n| Resistance (R) | 8 Ω |\n| Power Dissipated (P) | 1,800 W |", "Bottom line: When a 120 V power supply drives a 15 A current through a resistor of 8 Ω, it dissipates 1,800 watts of power. Proper engineering ensures safe and efficient operation under such high-power conditions.", "---", "Keywords: 120V resistor current 15A, power dissipation formula, Ohm’s Law, electrical resistance, power calculation, resistor heating, watt dissipation in resistors"]
