The bulbs connected in parallel would run the battery down faster because the total resistance of the circuit would be less than if they were connected in series. The reason the total resistance is lower when the bulbs are connected in parallel is simply because there are more paths available for the current to flow. If you keep adding more bulbs (resistance) in parallel, then you are creating more paths in which the current can flow. Since the the total current is higher because of the decreased resistance, the rate at which the energy of the battery is converted to light and heat is higher. Energy/Time equals Power. Power is the rate at which energy is converted. Power is also equivalent to the product of Voltage and Current. P=EI. As you can see here, Power is directly proportional to current and voltage. In this case we are only concerned with the change in current since the voltage of the battery is constant.
In a series circuit, there is only one path for current and as you add more resistances in series, you are restricting the flow of current through that one path. As you add more bulbs in series the total resistance increases, the current decreases, thus power or the rate of energy conversion decreases. The same amount of energy will be converted in this case but at a slower rate. You'll notice as you add more bulbs in series, all the bulbs will get dimmer. This is because the current is always the same at all points in a series circuit due to there only being one path for current flow. If you increase the resistance by adding more bulbs, the current decreases through each bulb. The rate at which energy is converted by each bulb is less. If you measure the voltage across each bulb in series, you will see that as more bulbs are added, the voltage across each bulb decreases. E=I*R. Since current through each bulb is less, voltage at each bulb is less. Given that each bulb has the same resistance, the total voltage of the source will be divided evenly across each bulb.
Ideally, as more bulbs are added in parallel the bulbs will not grow dimmer. When resistances are added in parallel, the voltage that is applied across each resistance is equal to the source voltage. Since the voltage is the same across each bulb in parallel, the current through each bulb is the same. The power dissipated is the same. As more bulbs are added, the total current of the circuit will increase as stated before but the current in the individual bulbs stays the same.
In practice, the bulbs will get a little dimmer when added in parallel. It's not nearly as pronounced as in the series case. Batteries have an internal resistance which affect things:
Chi Meson:If so, then this has to do with the internal resistance of the battery (or other voltage source). Since more current is drawn through he circuit, the internal resistance (little "r" usually) will cause a voltage drop that is proportional to the current. This means that some of the potential difference of the battery (the original "emf") is used up inside the battery (V=Ir) causing the remaining potential difference to be less than emf.
This is why, inexplicably to some teachers, bulbs connected in parallel keep getting dimmer with each bulb added, contrary to what they just taught.
https://www.physicsforums.com/showthread.php?s=&threadid=7508
That thread should help you understand as well.
For series circuits, the sum of the voltage drops across each component equal the source voltage. The current is the same through all components. As new components are added, the total resistance increases. The current decreases.
For parallel circuits, the sum of the current through each individual component equals the total current of the circuit. The voltage at each component is the same. As new components are added, the total resistance decreases and the total current increases.
