220V, 50 Hz AC supply is connected across a resistor of 50 k ohms. The current at time t Seconds, assuming that it is zero at t = O, is?
Correct answer: C. 6.2 sin(314t) mA
- A. 4.4 sin(314t) mA
- B. 4.4 sin(157t) mA
- C. 6.2 sin(314t) mA
- D. 6.2 sin(157t) mA
Explanation
The correct answer is 6.2 sin(314t) mA. The root mean square voltage (VRMS) of 220V is used to find the peak voltage (Vmax), which is 220√2 volts. The peak current (Imax) is then calculated using Ohm's law, Imax = Vmax/R. Substituting the values results in Imax being 6.2 mA. The angular frequency in radians per second is given by 2πf, where the frequency (f) is 50 Hz, resulting in 314 rad/s. Thus, the expression for the current as a function of time is i = 6.2 sin(314t) mA.Other options are incorrect due to errors in amplitude or frequency. For example, options with 4.4 mA have incorrect amplitude calculations, and those with 157t have incorrect frequency calculations.
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Alternating current varies periodically, so phase relationships become essential when current passes through a resistor, capacitor or inductor. The chapter distinguishes resistance from capacitive and inductive reactance, explains phase lead and lag, and connects changing electric and magnetic fields with the production and properties of electromagnetic waves.
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