Potomac Electric Power Co. yesterday reported that it earned $35.5 million (67 cents a share) on revenue of $305.6 million for its second quarter, up from $32.4 million (60 cents) on revenue of $259.7 million in the same period last year.

In the first half of this year, the Washington-based electric utility company earned $70.4 million ($1.33) on revenue of $595.7 million, compared with income of $66.6 million ($1.24) on revenue of $524 million for the first half of 1984.

* Washington-based First American Bank, N.A. reported second-quarter income of $2.2 million (95 cents a share) compared with $1.7 million (75 cents) for the same period in 1984. Income rose 21 percent from $3.2 million ($1.42) for the first six months of 1984 to $3.9 million ($1.73) for the first six months of this year.

At the end of the second quarter, assets were $1.2 billion, while at the end of the same quarter last year, assets were $1.09 billion.

First American is a member of First American Bankshares Inc., a Washington-based holding company that owns banks in New York and Tennessee and the three First American Bank companies in the District, Maryland and Virginia.

* D.C. National Bancorp Inc., parent company of D.C. National Bank, reported a 24 percent jump in second-quarter profits, to $961,000 ($1.08 a share) from $772,000 (96 cents) in the second quarter last year. For the first six months of this year, net income increased 24 percent, to $1.9 million ($2.14) from $1.5 million ($2.12) for the first six months of 1984.

The bank reported that assets rose by 32 percent in the first half of this year.