Will there be more power consumption to heat water in the tank if one of the elements is not working or will it just take twice as long to heat the same amount of water to a preset temperature?
It depends on which element is bad.
Water is drawn off the top of the water heater, a dip tube brings cold water to near the bottom. This is done because heat rises, so as the water is heated the hot water works it's way down to the bottom.
An electric tank style water heater uses two elements that work in sequence. As hot water is used the top element kicks on, if a lot is used then the temperature falls lower and lower inside the tank. As the temp drops physically in the tank the upper thermostat flips down to turn on the lower thermostat turning on the lower element. Once the lower portion is satisfied then it flips back up to turn on the upper element. Once that is satisfied the unit turns off.
So...... if the usage is low, like one person and short showers, and the lower element is bad, you may never even know it since you may hardly ever use enough hot water to turn on the lower element. If the upper element is bad then you may never have enough properly hot water at all.
So it is really not a matter of losing one out of two elements will take twice as long. It is much more complicated than that.
Twice as long (approximately). Each heating element adds heat at the same rate but the volume of water is constant.
The real issue is that when you start using hot water, the heater may not be able to heat up the replacement water quickly enough, meaning that your second shower may be uncomfortably cold.