The water analogy for electricity is a very good one, although not perfect. However you need to apply it carefully.
A circuit is similar to a closed loop of pipe. A closer analogy of a battery is a pump, not a bucket. Here are a couple rough diagrams illustrating the point.
Each pump can increase the water pressure (voltage) in the system.
The total pressure available at the motor is the sum of all the pressures that each pump contributes.
With a series connection all the water in the pipe must flow through each pump.
Turn any pump off and the flow is blocked and no water flows in the loop.
Running pumps at different duty cycles does no good since no water can flow unless all the pumps are on at the same time.
The water in the pipe drives a motor.
The amount of work done by the motor is the water pressure x amount of water.
Double the pressure and you double the power out of the motor.
Halve the amount of water that flows through it (say by turning the pumps off 50% of the time) and you halve the power out.
In the Parallel case:
You CAN run the pumps at different duty cycles as their ability to pump water is not restricted by the other pumps.
BUT you cannot have a system pressure more than the pressure you can get out of a single pump (1 cell voltage). You can flow more water though.
A circuit is similar to a closed loop of pipe. A closer analogy of a battery is a pump, not a bucket. Here are a couple rough diagrams illustrating the point.
Each pump can increase the water pressure (voltage) in the system.
The total pressure available at the motor is the sum of all the pressures that each pump contributes.
With a series connection all the water in the pipe must flow through each pump.
Turn any pump off and the flow is blocked and no water flows in the loop.
Running pumps at different duty cycles does no good since no water can flow unless all the pumps are on at the same time.
The water in the pipe drives a motor.
The amount of work done by the motor is the water pressure x amount of water.
Double the pressure and you double the power out of the motor.
Halve the amount of water that flows through it (say by turning the pumps off 50% of the time) and you halve the power out.
In the Parallel case:
You CAN run the pumps at different duty cycles as their ability to pump water is not restricted by the other pumps.
BUT you cannot have a system pressure more than the pressure you can get out of a single pump (1 cell voltage). You can flow more water though.