When connecting two batteries in series the voltage is increased. For example: Connecting two 5V batteries in series will produce 10V voltage but the current will be the same.
According to Ohm's Law V = IR the voltage is directly proportional to the current. Then why is the current not increases when voltage is increased?
If you model a battery as an ideal voltage source in series with a resistance, then putting batteries in series will increase the open-circuit voltage by n times the number of batteries in series, but the short-circuit current will not change because the internal resistance also increases by n times.
For more moderate loads than a short circuit the current will increase with the number of batteries. For example, if your battery has a 1.5V voltage and a 1 ohm source resistance and you connect 100 in series you will have 150V and 100 ohms source resistance. Connecting them to a 1000 ohm resistor will give you 136mA (150V/1100 ohms). One battery across 1000 ohms will result in a current of a bit under 1.5mA (1.5V/1001 ohms).
Batteries don't quite behave like voltage sources with fixed resistors in series-- the internal resistance changes with battery condition, temperature and history of discharge, but it's a reasonable first approximation.
If you connect two same batteries in series you're doubling the voltage while keeping the same capacity(Ah) rating. But if you're connecting batteries in parallel you are in fact doubling the capacity of the battery while maintaining the voltage same as one of the individual batteries.
Think of a battery as a water reservoir which has a valve attached to it. The water storage has a certain capacity like a battery. If you open the valve you can let in some flow of water. Similarly, if you hook up a battery to a load there will be some current going out of it. As time goes on the reservoir discharges more and more, much the same way a battery behaves.
A battery doesn't follow Ohm's law. This law only applies to linear resistive loads. A battery has a voltage and a rated capacity. When no load is connected to it there will be no current coming out of it. But if you connect a load such as a resistor across its terminals it'll be going to draw some amount of current according to Ohm's law. This is true for any other load with its own I-V characteristic.
