27 charges of equal values are combined together to make a large charge. It the potential of each charge is 5 V, then the potential of the big charge will be:

Options

A. 40 V
B. 45 V
C. 50 V
D. 55 V

Explanation

To solve the problem, we need to determine the potential of a large charge formed by combining 27 smaller charges, each with a potential of 5 V. Here’s a step-by-step solution:

### Step 1: Understand the relationship between charge and potential
The potential \( V \) of a point charge is given by the formula:
\[ V = \frac{kQ}{r} \]
where \( k \) is Coulomb's constant, \( Q \) is the charge, and \( r \) is the distance from the charge.

### Step 2: Define the charges
Let the charge of each smaller charge be \( Q \). Since there are 27 such charges, the total charge \( Q' \) of the larger charge will be:
\[ Q' = 27Q \]

### Step 3: Relate the radii of the charges
When combining the charges, we assume that the smaller charges are combined into a larger spherical charge. If the radius of each smaller charge is \( r \), then the radius of the larger charge \( R \) can be derived from the volume relationship:
\[ \text{Volume of smaller charge} = \frac{4}{3} \pi r^3 \]
\[ \text{Volume of larger charge} = \frac{4}{3} \pi R^3 \]
Since the total volume of the smaller charges equals the volume of the larger charge:
\[ 27 \left(\frac{4}{3} \pi r^3\right) = \frac{4}{3} \pi R^3 \]
Cancelling \( \frac{4}{3} \pi \) from both sides gives:
\[ 27r^3 = R^3 \]
Taking the cube root of both sides:
\[ R = 3r \]

### Step 4: Calculate the potential of the larger charge
The potential of the larger charge \( V' \) can be expressed as:
\[ V' = \frac{kQ'}{R} = \frac{k(27Q)}{R} \]
Substituting \( R = 3r \):
\[ V' = \frac{k(27Q)}{3r} = 9 \cdot \frac{kQ}{r} \]

### Step 5: Substitute the known potential
We know that the potential of each smaller charge is 5 V:
\[ \frac{kQ}{r} = 5 \, \text{V} \]
Thus, substituting this into the equation for \( V' \):
\[ V' = 9 \cdot 5 = 45 \, \text{V} \]

### Conclusion
The potential of the larger charge formed by combining 27 smaller charges, each with a potential of 5 V, is:
\[ \boxed{45 \, \text{V}} \]