A capacitor of capacitance C is connected to a battery of voltage V. If the batt
Practice Questions
Q1
A capacitor of capacitance C is connected to a battery of voltage V. If the battery is removed and the capacitor is connected to another capacitor of capacitance 2C, what is the final voltage across the combination?
V/3
V/2
V
2V
Questions & Step-by-Step Solutions
A capacitor of capacitance C is connected to a battery of voltage V. If the battery is removed and the capacitor is connected to another capacitor of capacitance 2C, what is the final voltage across the combination?
Correct Answer: V/3
Step 1: Understand that a capacitor stores charge. When the capacitor of capacitance C is connected to a battery of voltage V, it gets charged to a voltage V.
Step 2: Calculate the charge (Q) on the capacitor C using the formula Q = C * V.
Step 3: When the battery is removed, the charge Q remains on the capacitor C.
Step 4: Now, connect the charged capacitor C to another uncharged capacitor of capacitance 2C.
Step 5: The total charge (Q_total) remains the same, which is Q = C * V.
Step 6: The two capacitors (C and 2C) are now in parallel, so we need to find the equivalent capacitance (C_eq). The formula for equivalent capacitance in parallel is C_eq = C + 2C = 3C.
Step 7: The final voltage (V_final) across the combination can be found using the formula V_final = Q_total / C_eq.
Step 8: Substitute Q_total = C * V and C_eq = 3C into the formula: V_final = (C * V) / (3C).
Step 9: Simplify the equation: V_final = V / 3.
Capacitance and Charge Distribution – Understanding how charge is distributed between capacitors when connected in parallel or series.
Voltage and Energy Conservation – Applying the principle of conservation of charge and energy when capacitors are connected.
