If a 12 volt parallel circuit has 4 lamps and each lamp consumes 1 amp what is the resistance of each lamp?

Two or more switches in series form a logical AND; the circuit only carries current if all switches are 'on'. See AND gate. A battery is a collection of electrochemical cells.

If the cells are connected in series, the voltage of the battery will be the sum of the cell voltages. For example, a 12 volt car battery contains six 2-volt cells connected in series. If two or more components are connected in parallel they have the same potential difference (voltage) across their ends.

The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applicable to all circuit components connected in parallel. The total current is the sum of the currents through the individual components, in accordance with Kirchhoff’s current law.

In a parallel circuit the voltage is the same for all elements. The current in each individual resistor is found by Ohm's law. To find the total resistance of all components, add the reciprocals of the resistances of each component and take the reciprocal of the sum.

This sometimes goes by the mnemonic "product over sum". An old term for devices connected in parallel is multiple, such as a multiple connection for arc lamps. The relations for total conductance and resistance stand in a complementary relationship: the expression for a series connection of resistances is the same as for parallel connection of conductances, and vice versa.

If the inductors are situated in each other's magnetic fields, this approach is invalid due to mutual inductance. The sign of depends on how the magnetic fields influence each other.