Question

in which system will the bulb(s) shine brightest?
a circuit with one battery and one bulb.
a circuit with two batteries and two bulbs.
a circuit with three batteries and one bulb.
a circuit with two batteries and one bulb.

Explanation:

Step1: Recall the relationship between voltage and bulb brightness

The brightness of a bulb is related to the power it receives. Power \(P = \frac{V^{2}}{R}\) (assuming the resistance \(R\) of the bulb is constant). The higher the voltage \(V\) across the bulb, the brighter the bulb.

Step2: Analyze each circuit

• For a circuit with one battery and one bulb: Let the voltage of one battery be \(V\), so the voltage across the bulb is \(V\).
• For a circuit with two batteries and two bulbs (assuming batteries are in series and bulbs are in series): The total voltage of two - series batteries is \(2V\). If two bulbs are in series, the voltage across each bulb is \(V\) (using the voltage - division rule \(V_{bulb}=\frac{R}{R + R}\times2V=V\)).
• For a circuit with three batteries and one bulb: If three batteries are in series, the total voltage is \(3V\), and the voltage across the single bulb is \(3V\).
• For a circuit with two batteries and one bulb: If two batteries are in series, the total voltage is \(2V\), and the voltage across the single bulb is \(2V\).

Since \(3V>2V > V\) (from the power formula \(P=\frac{V^{2}}{R}\), when \(R\) is constant, \(P\) is proportional to \(V^{2}\)), the bulb in the circuit with three batteries and one bulb will have the highest power.

Answer:

A circuit with three batteries and one bulb.