Atlantic Research Corp. has reported a 28 percent increase in first-quarter profits, rising to $751,000 (41 cents a share), up from $585,000 (39 cents) in the 1980 first quarter.

The Alexandria-based scientific research firm said sales rose 27 percent from $17 million for the first quarter last year to $21.6 million this year.

In other reports, Baltimore Gas & Electric Co. reported a sharp rise in profits for the quarter ended March 31, to $43.4 million ($1.32 a share) compared with profits of $29.3 million (92 cents) for the same quarter in 1980. Sales rose to $384.4 million compared with 1980 first-quarter sales of $316 million.

Bank of Virginia Co. reported a 15 percent drop in profits before securities transactions, as first-quarter profits fell to $2.7 million (50 cents a share) from $3.2 million (60 cents).

But the bank also said that assets rose 10 percent, climbing to $2.58 billion at the end of the quarter, compared with $2.34 billion at the end of the 1980 first quarter. Deposits rose from $1.71 billion at the end of the 1980 first quarter to $1.8 billion this year.

Carl M. Freeman Associates, a Potomac residential and commercial developer, reported 1980 profits of $2 million ($1.51 a share), compared with 1979 profits of $2.2 million ($1.55). Total revenues declined to $16.8 million for 1980, compared with 1979 revenues of $19.4 million.