A battery has e.m.f. 4 V and internal resistance r . When this battery is connected to an external resistance of 2 ohms , a current of 1 amp . flows in the circuit. How much current will flow if the terminals of the battery are connected directly

Options

A. 1 amp
B. 2 amp
C. 4 amp
D. Infinite

Answer

To solve the problem step by step, we will first analyze the given information and then calculate the required current when the battery is connected directly.

### Step 1: Understand the given data
- The electromotive force (e.m.f) of the battery, \( E = 4 \, \text{V} \)
- External resistance, \( R = 2 \, \Omega \)
- Current flowing through the circuit with the external resistance, \( I = 1 \, \text{A} \)

### Step 2: Use Ohm's law to find the internal resistance
When the battery is connected to the external resistance, the total voltage across the circuit is equal to the e.m.f of the battery, which can be expressed using Ohm's law:

\[ I = \frac{E}{R + r} \]

Where:
- \( I \) is the current (1 A)
- \( E \) is the e.m.f (4 V)
- \( R \) is the external resistance (2 Ω)
- \( r \) is the internal resistance of the battery

Substituting the known values into the equation:

\[ 1 = \frac{4}{2 + r} \]

### Step 3: Solve for internal resistance \( r \)
Rearranging the equation to find \( r \):

\[ 2 + r = \frac{4}{1} \]
\[ 2 + r = 4 \]
\[ r = 4 - 2 \]
\[ r = 2 \, \Omega \]

### Step 4: Calculate the current when the battery is connected directly
When the terminals of the battery are connected directly, the only resistance in the circuit is the internal resistance \( r \). The current \( I' \) can be calculated using Ohm's law again:

\[ I' = \frac{E}{r} \]

Substituting the values:

\[ I' = \frac{4}{2} \]
\[ I' = 2 \, \text{A} \]

### Conclusion
When the terminals of the battery are connected directly, a current of \( 2 \, \text{A} \) will flow.

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