a 100picofarad capacitor is charged to potentiAl difference of 24v.it is connected to uncharged capacitor of capacitance 20 pico farad .what is new potential diff.across 100pF capacitor?

To find the new potential difference across the 100 picofarad (pF) capacitor after it is connected to an uncharged 20 pF capacitor, we can use the principle of charge conservation. When the two capacitors are connected, the total charge will redistribute between them, and we can calculate the new voltage across the 100 pF capacitor.

Understanding Capacitor Basics

A capacitor stores electrical energy in the form of an electric field. The charge (Q) stored in a capacitor is given by the formula:

Q = C × V

where C is the capacitance in farads and V is the voltage across the capacitor.

Initial Charge on the 100 pF Capacitor

Initially, the 100 pF capacitor is charged to a potential difference of 24 volts. We can calculate the initial charge (Q_initial) on this capacitor:

Q_initial = C × V = 100 pF × 24 V = 100 × 10^-12 F × 24 V = 2.4 × 10^-9 C

Connecting the Capacitors

When the charged 100 pF capacitor is connected to the uncharged 20 pF capacitor, the total charge remains the same, but it will now be shared between both capacitors. The total capacitance (C_total) when connected in parallel is:

C_total = C1 + C2 = 100 pF + 20 pF = 120 pF

Finding the New Voltage

After the connection, the total charge (Q_total) remains 2.4 × 10^-9 C, and we can find the new voltage (V_new) across both capacitors using the formula:

V_new = Q_total / C_total

Substituting the values we have:

V_new = 2.4 × 10^-9 C / 120 × 10^-12 F = 20 V

Final Result

The new potential difference across the 100 pF capacitor after it is connected to the uncharged 20 pF capacitor is 20 volts. This demonstrates how charge redistributes in a circuit when capacitors are connected together, and it highlights the importance of understanding capacitance and voltage relationships in electrical circuits.