The profits obtained by a foreign firm's branch in India are recorded on the debit side of the current account in the balance of payments for the following reasons:

1. Current Account: The current account of the balance of payments tracks transactions related to the export and import of goods and services, as well as income received from or paid to foreign entities. It includes items like trade in goods, trade in services, and income earned from investments, among other things.

2. Profits from a Foreign Firm's Branch: When a foreign firm's branch in India earns profits, it represents income earned within the Indian territory. These profits are considered a credit item in the current account because they reflect income received from providing services or conducting business activities within India. This income adds to the country's foreign exchange reserves and is recorded on the credit side because it represents a positive inflow of funds into the country.

3. Credit Side: In the balance of payments, the credit side records all sources of income and funds flowing into the country, while the debit side records all sources of payments and funds flowing out of the country. When a foreign firm's branch in India earns profits, it is considered income inflow, and thus it is recorded on the credit side.

So, profits obtained by a foreign firm's branch in India are recorded on the credit side of the current account in the balance of payments to reflect the positive income earned from their operations within India.