An $$RC$$ circuit as shown in the figure is driven by a $$AC$$ source generating a square wave. The output wave pattern monitored by $$CRO$$ would look close to:

We need to find the output wave pattern monitored by a CRO for a series $$RC$$ circuit driven by an AC source generating a square wave, where the output is taken across the capacitor ($$C$$).

When a square wave voltage is applied to an $$RC$$ circuit, the input voltage alternates between a constant high value and a constant low value. The behavior of the voltage across the capacitor ($$V_C$$) is governed by the processes of charging and discharging through the resistor ($$R$$):

1. During the Positive Half-Cycle of the Square Wave (Charging Phase):

• When the input voltage jumps to its maximum constant value, the capacitor does not instantly reach this voltage. Instead, it begins to charge up exponentially.
• The voltage across the capacitor rises according to the exponential charging formula: $$V_C(t) = V_0 \left(1 - e^{-\frac{t}{RC}}\right)$$.
• This results in a smooth, upward-curving (convex) profile that gradually flattens out as it approaches the peak input voltage.

2. During the Negative/Zero Half-Cycle of the Square Wave (Discharging Phase):

• When the input voltage drops instantly to zero or its minimum value, the capacitor begins to release its stored charge through the resistor.
• The voltage across the capacitor drops exponentially according to the discharging formula: $$V_C(t) = V_0 e^{-\frac{t}{RC}}$$.
• This results in a smooth, downward-sloping curve that decays rapidly at first and then tapers off.

Conclusion

Combining these alternating cycles, the waveform across the capacitor consists of repeating segments of exponential growth followed by exponential decay. This distinctive rounded, sawtooth-like appearance is characteristic of a low-pass filter integrating a square wave input.

Therefore, the output wave pattern monitored by the CRO closely matches Option A, which depicts these smooth exponential charging and discharging transitions.