Following are capsule summaries of crucial Senate contests decided yesterday.

North Carolina

In a race viewed as a referendum on the politics of the New Right, Sen. Jesse A. Helms (R-N.C.) rode the support of white voters to a surprisingly comfortable victory over the popular Gov. James B. Hunt Jr. Approximately 87 percent of the state's Black voters supported Hunt, while Helms collected about 60 percent of the white vote.

Helms is now in line to become chairman of the Senate Foreign Relations Committee, since Sen. Charles H. Percy (R-III.) appeared headed for defeat.

Helms trailed Hunt by as much as 20 points early in the campaign, but he recovered by moderating his vitriolic rhetoric and aligning himself closely with President Reagan. Together the candidates spent close to $25 million and involved celebrities from all walks of life in the campaign.

Hunt's governorship was also won by a Republican, Rep. James G. Martin, only the second Republican to capture the statehouse in the last century.

Illinois

Percy, a moderate Republican, lost a tight race to five-term Rep. Paul Simon. Fait polls showed Simon captured some 90 percent of the Illinois Black vote and two-thirds of the votes of those describing themselves as "liberals."

Simon, aged 55, is a prolific author who has sponsored civil rights and environmental legislation. During the campaign he capitalized on Percy's apparent opportunism, saying the Senator had moderated his once-liberal stances to more closely match the President's.

With 78 percent of the precincts reporting at 1 45 this morning, Simon led Percy by 51 to 48 percent.

Tennessee

Rep Albert Gore Jr (D-Tenn) a fiscal moderate with a reputation for inventive positions on the environment and arms control, had little trouble in this race to replace retiring Senate majority leader Howard H. Baker Jr (R-Tenn.)

Running against former State Sen. Victor Ashe, Gore successfully went against the grain of Reagan's two-to-one victory in the Tennessee Presidential voting. He became one of three Democrats to wrest a Senate seat from the GOP.

New Hampshire

Sen. Gordon J. Humphrey (R-N.H.) benefited perhaps more than any other candidate from the Reagan coattail effect, winning reelection by a 15-point margin over five-term Democratic Rep. Norman E. D'Amours.