A 500-ohm, 2-watt resistor and a 1500-ohm, 1-watt resistor are connected in parallel. What is the maximum voltage that can be applied across the parallel circuit without exceeding wattage ratings?

In a parallel circuit, the voltage across each component is the same. To determine the maximum voltage that can be applied without exceeding the wattage ratings of the resistors, we first need to identify the maximum power each resistor can safely dissipate.

The formula for power (P) in terms of voltage (V) and resistance (R) is given by:

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

For the 500-ohm resistor rated at 2 watts, we can rearrange the formula to solve for maximum voltage:

[ V = \sqrt{P \times R} ]

[ V = \sqrt{2 , \text{W} \times 500 , \Omega} ]

[ V = \sqrt{1000} ]

[ V = 31.62 , \text{V} ]

For the 1500-ohm resistor rated at 1 watt, we perform the same calculation:

[ V = \sqrt{P \times R} ]

[ V = \sqrt{1 , \text{W} \times 1500 , \Omega} ]

[ V = \sqrt{1500} ]

[ V =