Apple’s new iPad was supposed to usher in a new era of watching movies and television shows on the go. The “Retina Display” screen was so stunning, better than a high-definition TV, that some analysts wondered aloud whether owners would finally cut the cord to expensive cable services.

But hold off on the cable-cutting revolution. Apple’s vision for mobile entertainment has hit a snag.

Users quickly are discovering the new iPad gobbles data from cellular networks at a monstrous rate. Some find their monthly allotment can be eaten up after watching a two-hour movie. That has left consumers with a dilemma: Pay up for more data or hold back on using the device’s best features.

The quandary exposes a disconnect between the innovators of the latest mobile gadgets and the cellular companies that are struggling with strained networks and are now charging customers for each byte of data they consume. As smartphones and tablets have soared in popularity, Verizon Wireless and AT&T, the industry leaders, have stopped offering new customers unlimited data plans.

“My view has always been that video via cellular was always a fantasy,” said Craig Moffett, a senior analyst at Bernstein Research. “The networks simply aren’t designed to handle it.”

Earlier this month, Apple unveiled two kinds of iPads: one that only connects to WiFi signals and a more expensive model that also can link up to the latest and fastest cellular networks, called 4G. The latter allows a user to sit outdoors and, say, watch live NCAA basketball games in high-definition.

Users must pay at least $20 a month to use 1 gigabyte of data on Verizon’s 4G network or at least $14.99 for 250 megabytes with AT&T. Anything over those limits requires more money.

That concern put Garry Denny on a data diet. After paying $629 for an iPad that hooks up to Verizon’s 4G network, he quickly found that his tablet was a money guzzler.

In just 15 minutes last week, he watched a YouTube clip that ate nearly one-third of his $20 monthly wireless data plan. For perspective: That experience cost nearly $7, or the price of watching a matinee at a movie theater.

Denny bought the new iPad (the Apple fanatic has the two previous generations, too) because he wanted to watch television on business trips and stream movies anywhere he had coverage.

“It’s disappointing because I think of 4G as a way of taking the Internet and media anywhere to do anything I want at any time,” said Denny, the director of programming at Wisconsin Public Television. “But when you realize the heavy cost for that, it changes your perspective on how true that is.”

Connecting to 4G networks has become akin to jamming too many 18-wheelers on a highway with too few lanes, analysts say.

Cisco recently predicted that the global use of data over mobile devices will increase 18-fold over the next five years. And tablets put even more strain on wireless networking, generating three times more traffic than the average smartphone, according to Cisco’s study.

Wireless carriers have complained about their limitations. The companies moved to tiered data plans in recent years, saying they don’t have enough spectrum to build out their networks as fast as Americans are feeding their digital addictions.

The complaints have caught the attention of President Obama and Julius Genachowski, the chairman of the Federal Communications Commission, who supported putting more broadcast airwaves into the hands of commercial wireless carriers. But this may take years. In the short term, carriers have pursued audacious mergers. AT&T tried but failed to buy T-Mobile for $39 billion. Verizon Wireless, meanwhile, has a $3.6 billion proposal to buy airwaves from cable companies.

In response to customers frustrated by overloaded networks, the carriers have asked users to turn to WiFi networks as often as possible. They offer apps and tools to calculate data use so customers avoid penalty fees for going over the allotted monthly plans. The new iPad automatically defaults to WiFi networks, which is how most tablet owners connect to the Web, according to analysts.

“We’re helping our customers use their new iPad or any 4G LTE tablet in ways that extend their data plans,” Verizon Wireless spokeswoman Debra Lewis said.

AT&T and Apple declined to comment for this story.

The newest networks aren’t strained yet, but carriers have threatened to slow download speeds for the heaviest users. The policy is partly an effort to avoid the embarrassment AT&T faced in 2007, when its network in New York and San Francisco was overloaded by a deluge of traffic created by the iPhone.

“For the time being, it looks like consumers who are budget-conscious will need to reserve some of their high-bandwidth applications for times they are at home or connected to a WiFi network,” said Michael Calabrese, director of the future of wireless project at the New America Foundation think tank.