In the circuit shown below, the battery voltage is 12 volts and the light bulbs are all identical. What is the voltmeter reading?

Question

Series circuit and voltmeter
A. 0 volts
B. 3 volts
C. 4 volts
D. 12 volts

Answer 1

To solve for the voltmeter reading in a series circuit with identical light bulbs and a 12-volt battery, you can follow this reasoning:

1. Understanding Series Circuits: In a series circuit, the total voltage from the battery is distributed among all the components (in this case, identical light bulbs). The sum of the voltage drops across each component must equal the total voltage supplied by the battery.

2. Voltage Distribution: If the circuit has \( N \) identical light bulbs, the voltage drop across each bulb will be equal since they are identical. Therefore, the voltage drop across each bulb can be found using the formula:

   \[ V_{bulb} = \frac{V_{total}}{N} \]

   where \( V_{total} \) is the total voltage from the battery (12 volts).

3. Assumed Number of Bulbs: Since the number of light bulbs \( N \) is not specified in your query, it is generally common to assume cases such as:

   • 1 bulb: The voltmeter would read 12 volts across the single bulb.
   • 2 bulbs: The voltmeter would read 6 volts across each bulb (12V/2).
   • 3 bulbs: The voltmeter would read 4 volts across each bulb (12V/3).
   • 4 bulbs: The voltmeter would read 3 volts across each bulb (12V/4).
   • And so forth.

4. Reading of Voltmeter: If the voltmeter is measuring across only one of the bulbs:

   • If there is 1 bulb, reading = 12 volts.
   • If there are 2 bulbs, reading = 6 volts for each bulb.
   • If there are 3 bulbs, reading = 4 volts for each bulb.
   • If there are 4 bulbs, reading = 3 volts for each bulb.

Since the provided options are 0 volts, 3 volts, 4 volts, and 12 volts, without a specific number of bulbs mentioned, the possible readings that could match a typical assumption (assuming multiple bulbs) are either 3 volts or 4 volts.

If we consider a common scenario of 3 bulbs:

• For 3 bulbs, the voltmeter would read 4 volts since each would share the 12 volts equally.

Thus, without additional context on the number of bulbs in the series circuit, the likely reading would be 4 volts.

Therefore the option that corresponds best, provided that there are 3 identical bulbs would be:

C. 4 volts.