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The switch SW shown in the circuit is kept at position ‘1’ for a long duration. At t = 0+, the switch is moved to position ‘2’. Assuming |Vo2| > |Vo1|, the voltage v_c(t) across the capacitor is

1. v_c(t) = −Vo2(1 − e^(−t/2RC)) − Vo1
2. v_c(t) = Vo2(1 − e^(−t/2RC)) + Vo1
3. v_c(t) = −(Vo2 + Vo1)(1 − e^(−t/2RC)) − Vo1
4. v_c(t) = (Vo2 − Vo1)(1 − e^(−t/2RC)) + Vo1

Correct answer: v_c(t) = (Vo2 − Vo1)(1 − e^(−t/2RC)) + Vo1

Solution

The correct option describes the voltage across the capacitor as it transitions from an initial voltage Vo1 to a new voltage Vo2 after the switch is moved. The term (Vo2 - Vo1) represents the change in voltage, and the exponential factor accounts for the charging behavior of the capacitor over time, starting from Vo1.

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