In a victory for President Carter, the Senate Rules Committee voted 5 to 4 yesterday for public financing of Senate election campaigns, starting in 1978.

Across the Capitol, meanwhile, Speaker Thomas P. (Tip) O'Neill Jr., (D-Mass.) announced general Democratic agreement on three amendments aimed at removing HOuse objections to Carter's stalled electionday voter registration bill, and Majority Leader Kim Wright (D-Tex.) predicted that, too, would now pass.

Senate election financing, to be provided by the U.S. government, would be for the general elections campaign only, not for the primaries. The public money would be available to minor party candidates as well as Democratic and Republican candidates.

Public financing is already part of the law for presidential campaigns, and about $72 million was given to presidential candidates, in the 1976 race. President Carter, in one of several proposed changes in election laws, asked for extension of the public financing concept to congressional elections.

The Rules Committee bill covers only Senate races, but House proponents of public financing, who include the Speaker, will seek to provide it for House members when the House Administration Committee begins writing its own bill next month.

All Rules Committee Democrats except James B. Allen (D-Ala.) backed the bill. All Republican opposed it. Majority Leader Robert C. Byrd (D-W.Va.), who voted for it, said he hadn't considered yet when to schedule it for floor action. Sponsor Dick Clark (D-Iowa) said he hoped it would be before the August recess and claimed enough votes to break a possible GOP-Southern Democrat filibuster.

The bill sets overall spending limits for those candidates wishing to obtain Treasury financing for their Senate campaigns, and then provides that the Treasury would pay up to 62.5 per cent of the overall ceiling. The rest would have to be raised from private sources. Here is now the formula works:

The candidate's overall spending limit for the ganeral election would be $250,000 plus 10 cents for each person in the state of voting age. This ceiling works out to $532,000 for Maryland, $600,000 for Virginia, $1,478,000 for New York and $1.688,000 for California.

Immediately upon nomination by a major party, a Senate candidate would receive from the Treasury a payment equal to 25 per cent of his overall spending ceiling. Beyond that, the Treasury would match the first $100 of any private contributions on a dollar-for-dollar basis, with the proviso that the combined initial 25 per cent Treasury payment plus the added matching be limited to 62.5 per cent of the overall ceiling.

If the opponent of a publicly funded candidate doesn't choose to receive public funding, he is allowed to go over the spending ceiling for his state. In fact case, however, the publicly funded candidate can also go over the ceiling without losing his public money. In fact, he can receive additional 50-50 matching from the Treasury up to another 62.5 per cent of the original ceiling.

For minor party and independent candidates, the system is different, and somewhat more restrictive.

Clark aides estimated the cost for the Senate matching system at $15 million to $17 million each two years.

In an unrelated amendment to basic federal election law, the Rules Committee decided to require candidates for office to report the names of contributors only if they gave them $201 or more, intead of $101, thus easing existing disclosure rules.