Northern Virginia Savings and Loan Association of Arlington yesterday became the first Washington-area S&L to receive a federal bailout under the Federal Savings and Loan Insurance Corp.'s capital assistance program.

Northern Virginia received $1.25 million in promissory notes in exchange for net worth certificates to keep it solvent. The amount represents between 25 and 35 percent of its operating losses during the past six months.

Thus far, 11 savings and loans around the country have received a total of $5.2 million in notes. The cashless bailout, a provision of the Garn-St Germain Depository Institutions Act passed last fall, was designed to help S&Ls weather the crisis brought on by high interest rates.

Assistance is granted on a sliding scale as a percentage of operating losses during the past six months to institutions that could survive on their own for at least six months more.

The purpose is to pump up an S&L's bottom line, maintaining it closer to the statutory ratio of reserves to assets until interest rates subside and the yield on its portfolio matches its cost of funds.

Although the legislation originally was conceived as an emergency measure for hundreds of failing S&Ls, the time required to draft regulations and falling interest rates combined to temper its urgency. Far fewer S&Ls have applied than expected. The first recipients were announced at the end of May.

Northern Virginia, a federally insured, privately held stock institution, suffered severe financial problems during the recession. It experienced losses of $5.8 million in 1981, and in May 1982 it had to sell four of its branch offices to the Bank of Virginia to raise $7.75 million in capital. At the time, the S&L's president, Martin L. Schnider, expressed confidence that the transaction offered it a chance to solve its problems without government assistance. By the end of the first six months of 1982--the latest period for which information is publicly available--it had $6.9 million in net worth.

Northern Virginia received the second largest aid package, surpassed only by Shadow Lawn Savings and Loan Association of West Long Branch, N.J., which got $1.825 million.

Officials of Northern Virginia were unavailable for comment.