Question

problem 12: (6% of assignment value) you take two electric bulbs. bulb #1 is marked 20w and bulb #2 is 50w. they are designed to be used with usual household voltage. if you connect these bulbs in series to an outlet, which of the following is true? bulb #1 produces greater illumination. bulb #2 produces greater illumination. it is impossible to answer without knowing what is the voltage of battery. both bulbs produce the same illumination. hints: 4% deduction per hint. hints remaining: 2 submission(s) remaining: 3 submit hint feedback: 5% deduction per feedback. i give up! grade summary deductions potential submissions attempt(s) remaining 3% deduction per attempt detailed view

Explanation:

Step1: Recall power - resistance - current relationship in series circuit

In a series circuit, the current \(I\) is the same through all components. The power of a bulb is given by \(P = I^{2}R\) (where \(P\) is power, \(I\) is current and \(R\) is resistance). The resistance of a bulb can be calculated from \(P=\frac{V^{2}}{R}\) (for a given voltage \(V\)), so \(R=\frac{V^{2}}{P}\). For bulb #1 with \(P_1 = 20W\) and bulb #2 with \(P_2=50W\) (assuming they are designed for the same voltage \(V\) which is household voltage), \(R_1=\frac{V^{2}}{20}\) and \(R_2=\frac{V^{2}}{50}\), and \(R_1 > R_2\).

Step2: Analyze power in series circuit

Since \(P = I^{2}R\) and \(I\) is the same in series, the bulb with higher resistance will have more power dissipated in a series - connected circuit. Since \(R_1>R_2\), from \(P = I^{2}R\), bulb #1 (with higher resistance) will have more power dissipated and thus produce greater illumination.

Answer:

Bulb #1 produces greater illumination.