Thirty-four persons were arrested in the Capitol yesterday after a sit-in that was one of several protests held around the nation in response to Wednesday's House vote approving aid to the Nicaraguan rebels.

In Frederick, Md., Robert C. Burkett, 42, was arrested on a trespassing charge after a mock burial was held on the lawn of the home of Rep. Beverly Byron (D-Md.) in protest of her vote to approve the administration-backed package of aid to the rebels, known as contras.

In another protest, about 30 demonstrators disrupted a news briefing by White House spokesman Larry Speakes, in Santa Barbara, Calif., about 25 miles from the mountaintop ranch where President Reagan went for a vacation.

The Capitol protest, which was organized by the Washington area Pledge of Resistance, began about 10:30 a.m. in the Rotunda. Tourists were led from the area and watched from a distance.

The Rev. Jesse L. Jackson, who said he was there as a member of the Rainbow Coalition to show support, began applauding the protesters and was joined by a number of onlookers. Jackson, who left the Rotunda before the arrests were made about 11 a.m., led the protesters in prayer.

Capitol Police said the demonstrators were charged with unlawful entry. A group spokesman said they were given citations and released pending arraignment today in U.S. District Court.

Shouting "Reagan is a fascist" and carrying placards saying "Stop the war in Nicaragua," the protesters in Santa Barbara tried unsuccessfully to push their way into the hotel room used to brief reporters.