Question

predicting results with a circuit
a circuit contains two lamps connected in series. what would happen to the brightness of each lamp if two more lamps were added? explain.

Explanation:

Step1: Recall series - circuit properties

In a series - circuit, the total resistance $R_{total}=\sum_{i = 1}^{n}R_i$. When more lamps (resistors) are added, the total resistance increases.

Step2: Apply Ohm's law

Ohm's law is $I=\frac{V}{R_{total}}$. Since the voltage $V$ of the power - source is constant, as $R_{total}$ increases, the current $I$ in the circuit decreases.

Step3: Analyze power and brightness

The power dissipated in a resistor (lamp) is $P = I^{2}R$. Since the current $I$ in the circuit decreases and the resistance of each lamp $R$ remains the same (assuming the lamps' resistances are constant), the power dissipated in each lamp decreases. And the brightness of a lamp is related to the power dissipated in it. So the brightness of each lamp decreases.

Answer:

The brightness of each lamp would decrease. This is because when two more lamps are added in series, the total resistance of the circuit increases. According to Ohm's law ($I=\frac{V}{R_{total}}$), with a constant voltage source, the current in the circuit decreases. Since the power dissipated in each lamp is $P = I^{2}R$ and the resistance of each lamp remains constant while the current decreases, the power dissipated in each lamp decreases, resulting in a decrease in brightness.