If two sine waves of same frequency have a phase difference of pi radina, then

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when one wave reaches its maximum value, the other will reach its minimum value

Explanation: When two sine waves of the same frequency have a phase difference of $\pi$ radians (180 degrees), they are said to be in phase opposition or antiphase. In this state, the instantaneous value of one wave is exactly the negative of the instantaneous value of the other, meaning one reaches its positive peak when the other reaches its negative peak.

Working Principle: The instantaneous value of a sine wave is given by $v(t) = V_m \sin(\omega t + \phi)$. If two waves have a phase difference of $\pi$, one is $v_1(t) = V_m \sin(\omega t)$ and the other is $v_2(t) = V_m \sin(\omega t + \pi)$. Since $\sin(	heta + \pi) = -\sin(	heta)$, it follows that $v_2(t) = -V_m \sin(\omega t) = -v_1(t)$. Consequently, when $v_1(t)$ is at its maximum ($V_m$), $v_2(t)$ is at its minimum ($-V_m$).

Key Formulas: $v_1(t) = V_m \sin(\omega t)$; $v_2(t) = V_m \sin(\omega t + \pi) = -V_m \sin(\omega t)$

Key Points: A phase shift of $\pi$ radians corresponds to $180^\circ$.; Waves in antiphase completely cancel each other out if added (superposition).; Both waves maintain the same frequency and amplitude.

Advantages: Useful in destructive interference applications.; Fundamental concept in balanced three-phase systems and differential signaling.

Applications: Noise cancellation systems; Push-pull amplifier circuits; Inverter design

Additional Info: Option A is incorrect because one reaches a positive minimum (peak) while the other reaches a negative minimum (trough).. Option B is incorrect because when one is at its positive maximum, the other is at its negative maximum (minimum value).. A phase difference of $\pi$ is equivalent to a time delay of half a period, $T/2$.

Answer: C is correct — when one wave reaches its maximum value, the other reaches its minimum value because they are in antiphase.

Exam Tip: Always remember that a phase shift of $180^\circ$ ($\pi$ radians) effectively flips the sign of the waveform, which is critical when analyzing differential amplifier gain or bridge rectifier phasing.

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