What is the maximum DC or RMS voltage that may be connected across a 20 watt, 2000 ohm resistor?

To determine the maximum DC or RMS voltage that can be safely applied to a 20-watt, 2000-ohm resistor, you can use the power formula in conjunction with Ohm's Law. The power rating of the resistor indicates the maximum amount of electrical power it can dissipate without overheating, which in this case is 20 watts.

Using the formula for power:

[ P = \frac{V^2}{R} ]

where:

• ( P ) is the power in watts (20 watts),

• ( V ) is the voltage in volts,

• ( R ) is the resistance in ohms (2000 ohms).

Rearranging the formula to solve for voltage ( V ):

[ V^2 = P \times R ]

Inserting the values:

[ V^2 = 20 , \text{watts} \times 2000 , \text{ohms} ]

[ V^2 = 40000 ]

[ V = \sqrt{40000} ]

[ V = 200 , \text{volts} ]

This calculation shows that the maximum voltage that can be applied across the resistor without exceeding its power rating is