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An AC power supply is connected to a resistor R. TH RMS emf is VRMS. The current is i(t) = io cos(wt). For the data given below, determine (A) the RMS curren (B) the resistance, and (C) the average power deliver to the resistor. : io = 1.15 A; w = 270 rad/s; Vrms = 90 V

An AC power supply is connected to a resistor R. TH RMS emf is VRMS. The current is i(t) = io cos(wt). For the data given below, determine (A) the RMS curren (B) the resistance, and (C) the average power deliver to the resistor. : io = 1.15 A; w = 270 rad/s; Vrms = 90 V

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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An AC power supply is connected to a resistor \( R \). The RMS emf is \( V_{\text{RMS}} \). The current is \( i(t) = i_0 \cos(\omega t) \). For the data given below, determine (A) the RMS current, (B) the resistance, and (C) the average power delivered to the resistor. Data provided: \[ i_0 = 1.15 \, \text{A}; \, \omega = 270 \, \text{rad/s}; \, V_{\text{RMS}} = 90 \, \text{V} \] ### Solutions: A) Calculate the RMS current: \[ I_{\text{RMS}} = \frac{i_0}{\sqrt{2}} \] B) Determine the resistance: \[ R = \frac{V_{\text{RMS}}}{I_{\text{RMS}}} \] C) Calculate the average power delivered to the resistor: \[ P_{\text{avg}} = I_{\text{RMS}}^2 R \]
Transcribed Image Text:An AC power supply is connected to a resistor \( R \). The RMS emf is \( V_{\text{RMS}} \). The current is \( i(t) = i_0 \cos(\omega t) \). For the data given below, determine (A) the RMS current, (B) the resistance, and (C) the average power delivered to the resistor. Data provided: \[ i_0 = 1.15 \, \text{A}; \, \omega = 270 \, \text{rad/s}; \, V_{\text{RMS}} = 90 \, \text{V} \] ### Solutions: A) Calculate the RMS current: \[ I_{\text{RMS}} = \frac{i_0}{\sqrt{2}} \] B) Determine the resistance: \[ R = \frac{V_{\text{RMS}}}{I_{\text{RMS}}} \] C) Calculate the average power delivered to the resistor: \[ P_{\text{avg}} = I_{\text{RMS}}^2 R \]
Expert Solution
Step 1: Given and Required

Maximum value of current,

                        i subscript o space equals space 1.15 space A

Rms voltage,

                        V subscript r m s space end subscript space equals space 90 space V

We need to find,

a) The RMS current

b) Resistance

c) Power delivered

                               

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