A capacitor of capacity C is charged fully by a cell of emf V/2 and then it is
disconnected and again connected with a cell of emf V (+ve plate of capacitor with +ve terminal of cell and vice versa). The heat developed in connecting wire during charging by second cell is ??
To calculate the heat developed in the connecting wire during the charging process, we need to determine the charge transferred from the second cell to the capacitor. The heat generated in the wire is equal to the work done by the electric field in moving this charge.
Here are the steps to calculate the heat:
1. Find the initial and final charges on the capacitor.
- When the capacitor is fully charged by the first cell, it will have charge +Q (where Q is the maximum charge it can store).
- When the capacitor is reconnected to the second cell, let's say it acquires a final charge of +q.
2. Calculate the charge transferred from the second cell to the capacitor.
- Since charge is conserved, the charge transferred from the second cell is q - Q.
3. Determine the potential difference across the capacitor.
- The potential difference across the capacitor is the voltage of the second cell, V.
4. Use the formula for work done to find the heat generated in the wire, H.
- The work done, W, is equal to the product of the potential difference (V) and the charge transferred (q - Q): W = V * (q - Q).
- The heat generated, H, is equal to the work done: H = W.
By following these steps, you can calculate the heat developed in the connecting wire during the charging process with the second cell.