The pd across terminals of a cell is found to be 29 volt and 28 volt respectively when it delivers a current of 1 ampere and 2 ampere respectively. The emf and internal resistance of a cell are respectively

Options

A. `30V,2Omega`
B. `30V,1Omega`
C. `29V,1Omega`
D. `28V,2Omega`

Explanation

To solve the problem, we need to find the electromotive force (emf) and the internal resistance of a cell based on the given terminal voltages at different currents.

### Step-by-Step Solution:

1. **Understanding the Problem:**
We have two scenarios:
- When the current (I1) is 1 A, the terminal voltage (V1) is 29 V.
- When the current (I2) is 2 A, the terminal voltage (V2) is 28 V.

2. **Using the Formula for Terminal Voltage:**
The terminal voltage (V) can be expressed in terms of the emf (E) and internal resistance (r) as:
\[ V = E - Ir \]
Rearranging gives:
\[ E = V + Ir \]

3. **Setting Up Equations:**
For the first scenario (1 A):
\[ E = 29 + 1r \quad \text{(Equation 1)} \]
For the second scenario (2 A):
\[ E = 28 + 2r \quad \text{(Equation 2)} \]

4. **Equating the Two Expressions for E:**
Since both expressions equal E, we can set them equal to each other:
\[ 29 + 1r = 28 + 2r \]

5. **Solving for r:**
Rearranging the equation gives:
\[ 29 - 28 = 2r - 1r \]
\[ 1 = r \]
Thus, the internal resistance \( r = 1 \, \Omega \).

6. **Finding the Emf (E):**
Now, we can substitute \( r \) back into either Equation 1 or Equation 2 to find \( E \). Using Equation 1:
\[ E = 29 + 1 \cdot 1 = 30 \, V \]

### Final Answers:
- The emf of the cell \( E = 30 \, V \)
- The internal resistance \( r = 1 \, \Omega \)