A capacitor of capacitance C is charged to a voltage V and then connected in par
Practice Questions
Q1
A capacitor of capacitance C is charged to a voltage V and then connected in parallel with another uncharged capacitor of capacitance C. What is the final voltage across the capacitors?
V/2
V
2V
0
Questions & Step-by-Step Solutions
A capacitor of capacitance C is charged to a voltage V and then connected in parallel with another uncharged capacitor of capacitance C. What is the final voltage across the capacitors?
Correct Answer: V/2
Step 1: Understand that a capacitor stores electrical charge. The amount of charge (Q) stored in a capacitor is given by the formula Q = C * V, where C is the capacitance and V is the voltage.
Step 2: In this case, we have one capacitor (let's call it Capacitor 1) with capacitance C that is charged to a voltage V. So, the charge on Capacitor 1 is Q1 = C * V.
Step 3: Now, we connect Capacitor 1 in parallel with another uncharged capacitor (Capacitor 2) that also has capacitance C. Initially, Capacitor 2 has no charge (Q2 = 0).
Step 4: When the two capacitors are connected in parallel, the total charge in the system must be conserved. This means the total charge before connecting them (Q1) will be equal to the total charge after they are connected (Q_total).
Step 5: The total charge after connecting them is distributed across both capacitors. Since they are in parallel, they will have the same final voltage (let's call it V_final). The total charge can be expressed as Q_total = C * V_final + C * V_final = 2C * V_final.
Step 6: Set the total charge before and after equal to each other: C * V = 2C * V_final.
Step 7: Simplify the equation: V = 2 * V_final. Now, solve for V_final: V_final = V / 2.
Step 8: Therefore, the final voltage across both capacitors after they are connected in parallel is V/2.
Capacitance and Charge Conservation – The total charge before and after connecting capacitors in parallel remains constant, and the voltage across capacitors in parallel is the same.
Voltage Division in Parallel Capacitors – When two capacitors are connected in parallel, the voltage across them is determined by the total charge divided by the total capacitance.
