AC Voltage Applied to a Resistor

Yes. For a pure resistor, v = v_m sin wt gives i = (v_m/R) sin wt. Both terms have the same sin wt, so they cross zero together and peak together. The phase difference is 0. This is only true for a resistor. An inductor makes current lag by 90 degrees and a capacitor makes it lead by 90 degrees.

Yes, for a resistor Ohm's law works for both AC and DC. At every instant v = iR. It also holds for amplitudes (i_m = v_m/R) and for rms values (V = IR). This is why the resistor is the simplest AC element for NEET.

i_m is the peak (maximum) current and v_m is the peak voltage. Since R is constant, dividing the peak voltage by R gives the peak current. The same relation holds for rms values: I = V/R. R has no frequency dependence, so the current amplitude does not change if you change the AC frequency.

No. The average of the current over a full cycle is zero, but power depends on i^2 (Joule heating i^2 R), which is always positive. So there is real heating. The average power is P = (1/2) i_m^2 R = I^2 R, where I = i_m/sqrt(2) is the rms current.

Reactance comes from energy storage (magnetic field in an inductor, electric field in a capacitor) that pushes the current out of phase. A resistor only dissipates energy as heat, it stores none, so it introduces no phase shift and no reactance. Its opposition is just R at every frequency.

Zero. Voltage and current are perfectly in phase for a pure resistor connected to an AC source.

i_m = v_m / R, where v_m is the peak voltage and R is the resistance. In rms form, I = V / R.

P = I^2 R = (1/2) i_m^2 R, where I = i_m/sqrt(2) is the rms current. This is real heat, unlike a pure inductor or capacitor which dissipate zero average power.

No. Since resistance R does not depend on frequency (unlike reactance X_L or X_C), the peak current i_m = v_m/R stays the same at any frequency.

R = V^2/P = 220^2/100 = 484 ohm. Peak voltage v_m = sqrt(2) x 220 = 311 V. rms current I = P/V = 100/220 = 0.454 A. (NCERT Example 7.1.)