Let's analyze the question about connecting bulbs in a series circuit and calculate the number of bulbs needed.

The question asks how many bulbs, each rated at 2 V, should be connected in series to operate safely on a 110 V AC line. In a series circuit, electrical components are connected end-to-end, forming a single path for the current. A key characteristic of a series circuit is that the total voltage across the entire circuit is the sum of the voltages across each individual component.

Understanding Series Circuits and Voltage

In a series connection:

• The same current flows through every component.
• The total resistance is the sum of individual resistances (R_total = R₁ + R₂ + ...).
• The total voltage supplied by the source is divided among the components (V_total = V₁ + V₂ + ...).

In this problem, we have multiple bulbs connected in series across a 110 V AC supply. Each bulb is rated for a maximum voltage of 2 V. To ensure that each bulb operates at its rated voltage (or less, although here we assume they need to sum up to the total voltage for proper brightness), the sum of the voltage drops across all the bulbs must equal the total supply voltage.

Calculating the Number of Bulbs in Series

We are given:

• Voltage rating of each bulb (V_bulb) = 2 V
• Total supply voltage (V_total) = 110 V

Let 'n' be the number of bulbs connected in series.

In a series circuit, the total voltage is the sum of the voltages across each identical component. So, if there are 'n' bulbs each with a voltage drop of V_bulb, the total voltage V_total is given by:

\( V_{\text{total}} = n \times V_{\text{bulb}} \)

We can rearrange this formula to find the number of bulbs, 'n':

\( n = \frac{V_{\text{total}}}{V_{\text{bulb}}} \)

Now, let's substitute the given values into the formula:

\( n = \frac{110 \, \text{V}}{2 \, \text{V}} \)

\( n = 55 \)

Therefore, 55 bulbs, each rated at 2 V, need to be connected in series to be safely run on a 110 V AC line.

Summary of Calculation

Here is a quick summary of the calculation:

This calculation shows that connecting 55 bulbs in series allows the total 110 V supply voltage to be evenly distributed among them, with each bulb receiving approximately 2 V, which is within its rated voltage.

Revision Table: Series Circuit Concepts

Additional Information: AC Voltage

The question mentions a 110 V AC line. AC stands for Alternating Current. The voltage in an AC circuit constantly changes direction and magnitude over time. The 110 V value typically refers to the RMS (Root Mean Square) voltage. For simple calculations involving series voltage division with resistive loads like incandescent bulbs, treating the RMS voltage value directly in the calculation is appropriate, as the ratio of voltages across components remains constant over time, regardless of the instantaneous AC voltage value.