A battery of emf 15 V and internal resistance of `4Omega` is connected to a resistor. If the current in the circuit is 2A and the circuit is closed. Resistance of the resistor and terminal voltage of the battery will be

Options

A. `2.5Omega,6V`
B. `3.5Omega,6V`
C. `2.5Omega,7V`
D. `3.5Omega,7V`

Explanation

To solve the problem step by step, we will use Ohm's law and the concepts of internal resistance in a circuit.

### Step 1: Identify the known values
- EMF of the battery (E) = 15 V
- Internal resistance of the battery (r) = 4 Ω
- Current in the circuit (I) = 2 A

### Step 2: Write the formula for the total resistance in the circuit
The total resistance (R_total) in the circuit can be expressed as the sum of the internal resistance (r) and the external resistance (R):
\[ R_{total} = R + r \]

### Step 3: Apply Ohm's law
According to Ohm's law, the relationship between voltage (V), current (I), and resistance (R) is given by:
\[ V = I \cdot R_{total} \]
In this case, the total voltage is the EMF of the battery (E):
\[ E = I \cdot (R + r) \]

### Step 4: Substitute the known values into the equation
Substituting the known values into the equation:
\[ 15 = 2 \cdot (R + 4) \]

### Step 5: Solve for R
Now, we can simplify and solve for R:
1. Distribute the 2:
\[ 15 = 2R + 8 \]
2. Rearrange the equation:
\[ 2R = 15 - 8 \]
\[ 2R = 7 \]
3. Divide by 2:
\[ R = \frac{7}{2} = 3.5 \, \Omega \]

### Step 6: Calculate the terminal voltage (V)
The terminal voltage (V) of the battery can be calculated using the formula:
\[ V = E - I \cdot r \]
Substituting the known values:
\[ V = 15 - 2 \cdot 4 \]
\[ V = 15 - 8 \]
\[ V = 7 \, V \]

### Final Results
- The resistance of the resistor (R) is **3.5 Ω**.
- The terminal voltage of the battery (V) is **7 V**.