Two light bulbs of resistance R1 and R2 (>R1) are connected in a series. Which is brighter? What if they are connected in parallel?

Series circuit:

P = I^2 * R

The bulb with the highest resistance will receive the most power; and will,
therefore, be brighter.

Parallel circuit:
P = V * I

The lowest resistance will receive the
most power and will be brighter.

When two light bulbs of resistance R1 and R2 are connected in series, the same current flows through both bulbs. The brightness of a bulb is directly proportional to the power dissipated in it. Power can be calculated using the formula P = I^2 * R, where P is the power, I is the current, and R is the resistance.

Since the current is the same in both bulbs, the bulb with higher resistance will have a higher power dissipation and therefore will be brighter. Thus, bulb R2 will be brighter than bulb R1 in a series circuit.

On the other hand, when the same two light bulbs of resistance R1 and R2 are connected in parallel, the voltage across both bulbs is the same. Again, the brightness of a bulb is directly proportional to the power dissipated in it.

Since the voltage is the same across both bulbs, the bulb with lower resistance will have a higher power dissipation and therefore will be brighter. Thus, in a parallel circuit, bulb R1 will be brighter than bulb R2.

To determine which light bulb is brighter when two light bulbs of resistances R1 and R2 (> R1) are connected in series, we need to understand how resistance affects the brightness of a light bulb.

In a series circuit, the same current flows through each component. The brightness of a light bulb is directly proportional to the power it consumes, which can be calculated using the formula:

Power (P) = (Current (I))^2 x Resistance (R)

Since the current is the same for both light bulbs, the power consumed by each light bulb is directly proportional to its resistance. Therefore, the light bulb with the lower resistance will consume more power and appear brighter.

Hence, in this case, the light bulb with resistance R1 will be brighter than the light bulb with resistance R2 when they are connected in series.

Now, let's consider the scenario when the two light bulbs are connected in parallel. In a parallel circuit, the voltage across each component is the same, while the current is divided among the components.

The power consumed by each light bulb will again be given by:

Power (P) = (Current (I))^2 x Resistance (R)

Since the voltage is the same for both light bulbs, the current flowing through each light bulb will be inversely proportional to its resistance. Therefore, the light bulb with higher resistance will consume less current and appear dimmer.

Hence, when the two light bulbs are connected in parallel, the light bulb with resistance R2 will be dimmer than the light bulb with resistance R1.