The Voltage (In Volts) at an Electrical Outlet Is a Function

Essay

The voltage (in volts) at an electrical outlet is a function of time (in seconds) given by V(t) = V₀ cos(120 $\pi$ ) where V₀ is a constant representing the maximum voltage.(a) What is the average value of the voltage over one second?
(b) How many times does the voltage reach a maximum in one second?
(c) Define the new function $S ( t ) = ( V ( t ) ) ^ { 2 }$ . Compute $\overline{S}$ , the average value of $S ( t )$ over one cycle.(d) Instead of the average voltage, engineers use the root mean square $V _ { n m s } = \sqrt { \bar { S } }$ . Determine V_rms in terms of V₀.(e) The standard household voltage in the United Stated is 100 volts. This means that V_rms = 110. What is the value of V₀?