In which of the following arrangements of electrical circuits will the bulb (s) not light up , assuming that all the bulbs and dry cells are identical ?

Options

A.
B.
C.
D.

Explanation

To determine in which arrangements of electrical circuits the bulbs will not light up, we need to analyze each option provided in the question. Here’s a step-by-step solution:

### Step 1: Understand the Circuit Components
- We have identical bulbs and dry cells (batteries).
- A bulb lights up when there is a complete circuit allowing current to flow through it.

### Step 2: Analyze Each Circuit Arrangement
1. **Option 1**: Two dry cells connected in parallel with one bulb.
- In this arrangement, both cells can provide voltage to the bulb. Since the circuit is complete, the bulb will light up.

2. **Option 2**: Two bulbs connected in series with two dry cells.
- Here, the first bulb is connected to the first cell and the second bulb is connected to the second cell. The positive terminal of the first cell connects to the negative terminal of the second cell, allowing current to flow through both bulbs. Therefore, both bulbs will light up.

3. **Option 3**: Two dry cells connected in series with one bulb.
- In this case, the positive terminal of the first cell is connected to the negative terminal of the second cell, and the bulb is connected across the series combination of the two cells. This arrangement will also allow current to flow through the bulb, causing it to light up.

4. **Option 4**: A single dry cell connected to two bulbs in parallel.
- In this arrangement, the single cell can provide voltage to both bulbs. If the circuit is complete, both bulbs will light up.

### Step 3: Identify the Arrangement Where Bulbs Do Not Light Up
- After analyzing all the options, we find that in none of the arrangements described do the bulbs fail to light up. Each arrangement allows for a complete circuit, enabling current to flow.

### Conclusion
- Based on the analysis, all the options provided will allow the bulbs to light up. Therefore, there is no arrangement among the given options where the bulbs will not light up.