President Carter formally sent Congress yesterday a detailed version of his much-ballyhooed windfall profits tax that, despite the president's ringing rhetoric, would impose only a modest extra tax bite on the oil industry.

Figures made public at the White House showed that at its peak in 1982 the measure would required the oil industry to pay only $1.7 billion more in federal taxes than it otherwise would owe-on extra profits of roughly $14.5 billion.

Despite the relatively small extra tax burden, the White House launched the proposal with an almost unprecedented gusher of pomp and ceremony, including an Oval Office "signing" ceremony and a tough-sounding talk for television cameras.

Carter warned again about an expected move by oil-state legislators to tack on a "plowback" exemption for profits the oil companies spend on new exploration. He said that "any further plowback would be a travesty."

In his speech before the TV cameras, Carter said the profits tax was needed to prevent the oil industry from reaping "a huge bonanza." That bonanza of profits would result from Carter's decision to end controls on domestic oil prices.

And he again tried to portray the measure as part of a "classic confrontation" between the public and the oil industry. Actually, in part because the profits tax is such a mild one the industry has not fought it vigorously. The announcement came after Carter and leaders of the House Ways and Means Committee agreed on a common strategy for pushing the profits-tax measure through quickly to avoid an initial squabble over how to spend the proceeds.

The plan calls for the panel to consider the windfall profits tax separately in early May and then deal with other proposals to rebate some of it to the poor and enact tax credits for energy conservation.

Rep. Al Ullman (D-Ore.), chairman of the committee, predicted the profits tax could be sent to the floor "very rapidly." Ullman said he hoped to "avoid the plowback issue" until after the Senate acts on the bill.

Ullman's reference was to a plan by Sen. Russell B. Long (D-La.), chairman of the Senate Finance Committee, to tack on a plowback provision. Carter avoided several opportunities yesterday to say he would veto such a bill.

The measure the president proposed yesterday was in marked contrast to his recent speechmaking, in which he has been pledging a tough crackdown on windfall profits in the oil industry-a politically popular stand with voters.

The $1.7 billion figure represents the estimated net increase in federal taxes that the oil companies would pay in 1982, the first year that domestic oil prices would be fully decontrolled.

Technically, the windfall profits tax would bring in $766 million in 1980, $2.5 billion in 1981, $2.8 billion in 1982, $2 billion in 1983, $1.75 billion in 1984, and $1.5 billion in 1985-or more if prices rise more rapidly.

But Treasury officials confirmed that imposing a windfall profits tax would reduce the amount of regular federal income tax the oil companies would have to pay, because the profits tax would be dedutible as a business cost.

As a result, th net increase in federal taxes that the oil industry would have to pay would amount to$500 million in 1980, $1.5 billion in 1981, $1.7 billion in 1982, $1.2 billion in 1983 and $1 billion each in 1984 and 1985.

The projected windfall profits for the industry-before any federal or state taxes are taken out-was estimated at $5.8 billion for 1980, $11.5 billion in 1981, $14.5 billion in 1982, $15.1 billion in 1983, and rising to $20.4 billion in 1985.

Stuart E. Eizenstat, President Carter's chief domestic adviser, estimated that, over the first three years of the windfall profits tax, the oil industry would be left with $6 billion in after-tax profits to reinvest in new exploration.

Eizenstat said the increase in the industry's federal tax burdenend-including both the regular income tax and the proposed windfall profits tax-wouluod siphon off about 55 percent of the windfall the oil companies would reap.

Carter previously has described his windfall profits measure as a "50 percent" tax on increased earnings-a label most observers have taken to refer to the windfall profits tax alone.

The president's proposal yesterday included three new elements that the administration had not disclosed when it announced the broad outlines of the new profits tax on April 5:

The measure would not allow oil companies to claim a writeoff for percentage depletion on the so-called windfall portion of their earnings-only on the portion not covered by the new tax.

The bill would continue the windfall profits tax on "upper-tier" oil-essentially, all oil discovered since 1972-for a full 10 years, rather than phasing it out earlier as some analysts had expected.

The administration's treatment of "lower-tier" oil-basically, the petroleum from wells discovered before 1972-was somewhat tougher than had been expected. Prices here would be decontrolled at 1.5 percent a month.

As he promised in his April 5 message, Carter proposed formally that Congress set up a special "energy security trust fund" to use the revenues to rebate money to the poor, to finance mass transit and to spur energy supply. The money would come from the windfall profits tax and the additional income taxes oil companies will incur because of decontrol.

However, Carter left undecided the question of how to spend $2.5 billion of that fund in fiscal 1981 and $4.5 billion in fiscal 1982, and agreed not to seek congressional action on it until after the windfall profits tax has passed.