Question

a resistor, of resistance 47 , is damaged when it dissipates a power greater than 0.5W. determine the maximum voltage that can be applied without damaging the resistor​

Answer 1

The maximum voltage that can be applied without damaging the resistor is 4.85 V

Step-by-step explanation:

Electric Power in a Resistor

Given a resistor or resistance R connected to a circuit of voltage V carrying a current I. The relation between these three magnitudes is given by Ohm's Law:

V = R.I

The dissipated power P of a resistor can be calculated by the following equation, known as Joule's first law:

`P = I^2.R`

Solving the first equation for I:

`\displaystyle I=(V)/(R)`

Substituting in the second equation:

`\displaystyle P=(V^2)/(R^2).R`

Simplifying:

`\displaystyle P=(V^2)/(R)`

Solving for V:

`V=√(P.R)`

The resistor has a resistance of R=47Ω and can hold a maximum power of P=0.5 W, thus the maximum voltage is:

`V=√(0.5\cdot 47)`

`V=√(23.5)`

V = 4.85 V

The maximum voltage that can be applied without damaging the resistor is 4.85 V