Final answer:
The power dissipation of bulb A when the switch is open is given by the formula P = V² / R, using the battery voltage and the bulb resistance. When the switch is closed, the power dissipation must account for the voltage drop due to the battery's internal resistance. As for the switch, it dissipates minimal power whether open or closed.
Step-by-step explanation:
The power dissipation of bulb A when the switch is open can be determined by using the formula for power, P = V2 / R, where V is the voltage across the bulb and R is the resistance of the bulb. When the switch is open, bulb A gets the full voltage from the battery, so power is calculated based on the battery voltage and the bulb's resistance.
When the switch is closed, bulb A's brightness changes due to the internal resistance of the battery. To calculate the power dissipation of bulb A when the switch is closed, the total resistance in the circuit, including the internal resistance of the battery, must be accounted for. The new voltage across bulb A will be less than the battery's electromotive force (EMF) due to the voltage drop across the battery's internal resistance. The power dissipated by bulb A can be calculated using the revised voltage across it and the formula P = I2 R, where I is the current through the bulb, and R is the bulb's resistance.
As for the power dissipated by the switch, it is small whether the switch is open or closed. When the switch is open, no current flows through it, and thus no power is dissipated. When the switch is closed, it has nearly zero resistance, which results in a very small voltage drop across it and thus very little power dissipation (P = I2 r, where r is the switch's resistance).