D.C. City Council Chairman-elect David A. Clarke, trying to avoid the kind of divisive political battle that plagued the council two years ago, has nominated 10 of the council's 13 members to be committee chairmen, District Building sources said.

Clarke's proposal, which must be ratified by a simple majority of the council when he takes office in January, would add two committees to the council--already facing a potential deficit of $500,000 for the fiscal year that began in October.

Clarke is expected to discuss the appointments, new council rules and the budget problems -- which could lead to council staff cuts -- with the full council today during the second day of a "retreat" at the Howard Inn on Georgia Avenue NW.

Informed sources said Clarke will name Betty Ann Kane (D-At large) to chair a new committee on cable television, human rights and utilities. John L. Ray (D-At large) will be named to the Public Service and Consumer Affairs Committee now headed by Wilhelmina J. Rolark (D-Ward 8), who will take over Clarke's old post as head of the Judiciary Committee.

Kane and Ray, who both ran unsuccessfully against Mayor Marion Barry this year, presented a ticklish problem to Clarke, sources said. Outgoing Chairman Arrington Dixon passed both over for chairmanships, and was criticized for disregarding their seniority, contributing to a political row over his choices. Clarke said during his campaign that both should get chairmanships. But as a Barry ally on most issues, Clarke had to try to find a way to accommodate both Kane and Ray without giving them platforms from which to run for Barry's job -- or Clarke's -- in 1986.

The politically sensitive area of cable television, which the council controls, could prove useful to Kane. In addition, the city's Office of Human Rights has been frequently criticized for poor administration and could become a Kane target.

Ray's appointment will still give him oversight over a new superagency Barry is expected to create to handle all the city's now-scattered permit and licensing processes.

Clarke will name H.R. Crawford (D-Ward 7) to a new committee that would oversee the city's Recreation Department, libraries and "youth affairs." Libraries and recreation previously were under the Human Services Committee, which will still be headed by Polly Shackleton (D-Ward 3) and will maintain its jurisdiction over the city's largest agency, the Department of Human Services.

Charlene Drew Jarvis (D-Ward 4), will retain chairmanship of the Housing and Economic Development Committee. Jarvis, who also ran for mayor this year, was in danger of losing the housing area to another member, District Building sources said.

John A. Wilson (D-Ward 2), will remain chairman of the powerful Finance and Revenue Committee while Jerry A. Moore (R-At large) will retain the Committee on Transportation and Environmental Affairs. William R. Spaulding (D-Ward 5) will remain head of the Government Operations Committee.

Hilda H. Mason (Statehood-At large) also will remain head of the Education Committee under Clarke's plan, while Nadine P. Winter (D-Ward 6), will keep her largely ceremonial role as council chairman pro tem. However, Winter will regain the authority she once had to review confirmations that come before the council.

Frank Smith, elected to fill Clarke's seat in Ward 1, will not chair a committee.