The solar age quietly dawned in California, aided by shortages of energy and water - and by a big tax credit for residential solar installation.

While solar energy still seems a 21st Century phenomenon to the Carter administration and most of the nation, it has fast become a reality in California. Under the prodding of Gov. Edmund G. (Jerry) Brown's administration, other alternative technologies - notably geothermal and waste water recycling - also are coming rapidly into use.

Only last Wednesday, Brown arrived home from a meeting with eastern businessmen to announce that Grumman Corp. of Bethpage, N.Y., would build a $1 million plant in Corcoran, in the San Joaquin Valley, to turn out 1,000 residential solar heating systems a month. Grumman also is forming a wholly owned subsidiary in California to market solar collectors and wind turbines.

State architect Sym Van der Ryn says that two years ago in California only 25 homes had solar heating. Now there are "hundreds, perhaps thousands" and the estimate of the California Energy Commission is 170,000 homes within the next three years.

The biggest impetus for this growth has been legislation giving homeowners a tax credit of 55 per cent, to a maximum of $3,000, on the purchase and installation of a solar energy system, including insulation installed at the same time. The recently passed bill also provides a tax credit of 25 per cent to businesses where the cost of their solar energy system is more than $6,000.

Until now the main barrier to installation of a solar energy system has been the initial cost. The tax credit has cut that cost in half. Furthermore, the law is written so that taxpayers who do not have sufficient tax liability to use the full credit in one year can carry it over.

Present estimates are that tax credits will cost the state $87 million during the three-year life of the bill - in effect, an $87 million state subsidy for solar energy.

The legislation has encouraged builders such as John Whitcombe of Tandem Properities in Davis, 16 miles west of here, to launch a 149-unit subdivision in which 90 per cent of the homes will have solar water heaters and solar heating and cooling. In competition for the limited number of houses that the city of Davis allowed to be built, solar homes were given extra credit.

In this subdivision, solar collectors on the roof heat water in a tank to provide the hot water for the house. Some of the hot water is transferred to rods imbedded in the slab floor of the house to provide space heating.

On summer nights, the water in the floor rods, serves to air-condition the house by absorbing heat from the slab and pumping it up to the roof, where it is radiated into the atmosphere. Cool water is then circulated into the rods in the floor from another tank.

Solar-heated homes in this subdivision, where six prototype homes are now near completion, will cost about $43,000, with the solar unit and a conventional backup system included in the price. The entire system costs $5,500, and buyers will get a state tax credit of $2525, leaving a cost of $2,975. By comparison, a buyer of a conventional home in the same subdivision would pay about $2,000 for his normal heating-cooling system.

Alternative energy systems are advancing here on a number of other fronts, much faster than in the rest of the nation. Among the most promising:

Development of geothermal system, which now provides 600 meagawatts of electrical power in Califronia. Energy Commission Chairman Richard L. Maullin predicts that by 2000 geothermal steam will be provided to 20,000 megawatts of power, more than half the state's current energy use. San Diego Gas and Electric Co. is building a 45-megawatt experimental power plant that will extract hot steam brine from wells in the Imperial Valley and use it to generate energy.

Construction of a $100 million sun-powered electricity generator, the world.'s first, at Daggett in the Mojave Desert. This is a joint project of the Federal Energy Development, Southern California Edison Co. and the Los Angeles Department of Water and Power. It will produce 10,000 kilowatts of electricity from 130 acres of what is now alfalfa fields that will be covered with computer-guided mirrors.

Mounting interest in wind power, once a substantial source of energy in the rurual West. Southern California Edison is now allowing windmill customers to hook into the Edison grid system with a special coupler that automatically draws from the system when wind is insufficient for the home generator. The customer also gets credit for any excess electricity that he feeds into the Edison grid.

Increasing sale of energy-saving home designs, such as geodesic domes. An estimated 150 kits for building domes are sold every month in California, two-thirds of them by an Aptos firm known as Cathedralite Domes. The most popular kit, for a two-stoy 45-foot dome with 2,600 feet of living space, sells for $10,000.

Experiemental use of solar power in commercial heating. Gov. Brown last month dedicated a $250,000 system now in use at the Red Star Laundry in Fresno, and state officials are trying to convince various canners and food processors to follow suit.

Much of the push for alternative technologies has come from Brown and architect Van der Ryn. Van de Ryn and Bill Press, director of the Office of Planning and Research, have opposed efforts of state water officials to build large sewage treatment systems. Instead, they have advocated water recycling and biological treatment of sewage. They also have favored septic tanks in rural areas, which Press said has enabled the administration to make common cause with real estate agents and county supervisors against engineers who follow "the sewer imperative."

Meanwhile, the Energy Commission has used what Maulin calls "a carrot-and-stick approach" to alternative energy development.

"We've told the utility companies that in California you're not going to be penalized for experimenting," Maullin said. "On the other hand we're saying that approval of your pet projects is conditioned on keeping an open mind."

In practice this seems to mean that utilities seeking approval for nuclear-power projects face skepticism bordering on hostility, while they usually have strong support from the commission for geothermal or solar development.

Brown and his top aides have tried to set their own example. The governor had a solar water heater installed in his own apartment, several state buildings are being refitted for solar heating, and Van der Ryn has created a plan that could make Sacramento a national model of solar energy use in public buildings.

The plan features a six-story, $15 million office building of 250,000 square feet that will be heated and cooled by solar energy, making it the first such sizable office building in the world. It is scheduled for completion in 1980.

Chosen from 41 entries, the winning design, submitted by Benham, Blair & Affiliates of Los Angeles, calls for a sloping 25,000-square-foot solar energy collector covering one wall of the building. It is composed of hundred of dish-shaped reflectors that will automatically tilt to take advantage of the sun.

Most of the building is underground, a design which allowed the architects to include a small park in the above-ground segment.