Exercise:
The light bulb in circuit A has normal brightness. The batteries and light bulbs in circuits B to G have the same characteristics as the battery and light bulb in circuit A. For each of the light bulbs to decide whether their brighntess is normal i.e. the same as in circuit A higher than normal lower than normal or whether it is completely off. center includegraphicswidthmm#image_path:brightness-# center

Solution:
Since the current through a light bulb is a monotonic function of the voltage across the light bulb i.e. the current increases if and only if the voltage increases we only have to verify if either the voltage or the current changes. description item Light bulb : The standard voltage is split up between the two light bulbs. The voltage across light bulb is therefore lower than the standard voltage. Light bulb has less than normal brightness. item Light bulb : The total voltage is twice the standard voltage. It is split up between the two light bulbs. The voltage across light bulb is therefore the same as the standard voltage. Light bulb has normal brightness. item Light bulb : The total voltage is twice the standard voltage. It is split up between the two light bulbs. The voltage across light bulb is therefore the same as the standard voltage. Light bulb has normal brightness. item Light bulbs & : Light bulb is directly connected to the battery i.e. the voltage across light bulb corresponds to the standard voltage. The other two light bulbs are also connected to the standard voltage so the voltage across light bulb is only half the standard voltage. Therefore light bulb has normal brightness while light bulb has less than normal brightness. item Light bulbs & : Light bulb is connected to two batteries in series same polarity so the voltage is twice the standard voltage. Light bulb is in a loop with not battery. The potential before and after the light bulb is the same i.e. there is no potential difference across the light bulb. Therefore light bulb is brighter than normal while light bulb is off. item Light bulbs & : The outer loop contains two batteries same polarity and two light bulbs so the voltage across light bulb corresponds to the standard voltage. Since the two batteries and the two light bulbs have the same characteristics the potential between the two batteries is the same as the potential between the light bulbs to the left and right of the circuit so there is no potential difference across light bulb . Therefore light bulb has normal brightness while light bulb is off. item Light bulbs & : Light bulb is in a loop with both batteries same polarity so the voltage corresponds to twice the standard voltage. The light bulbs to the left and right of the circuit are each in a loop with a single battery so the voltage across light bulb corresponds to the standard voltage. Therefore light bulb is brighter than normal and light bulb has normal brightness. description