When connected across the terminals of a cell, a voltmeter measures 5 V and a connected ammeter measures 10 A of current. A resistance of 2 ohm s is connected across the terminals of the cell. The current flowing through this resistance will be

Explanation

To solve the problem step by step, we will follow the principles of Ohm's law and the current division rule.

### Step 1: Identify the given values
- Voltage (V) = 5 V
- Current (I) = 10 A
- Resistance (R) = 2 Ω (the resistance connected across the terminals of the cell)

### Step 2: Calculate the internal resistance of the cell
Using Ohm's law, which states that \( V = I \cdot R \), we can find the internal resistance (R_internal) of the cell.

\[ R_{\text{internal}} = \frac{V}{I} = \frac{5 \, \text{V}}{10 \, \text{A}} = 0.5 \, \Omega \]

### Step 3: Determine the total resistance in the circuit
The internal resistance of the cell (0.5 Ω) and the external resistance (2 Ω) are in parallel. The formula for the equivalent resistance (R_eq) of two resistors in parallel is given by:

\[ \frac{1}{R_{\text{eq}}} = \frac{1}{R_{\text{internal}}} + \frac{1}{R_{\text{external}}} \]

Substituting the values we have:

\[ \frac{1}{R_{\text{eq}}} = \frac{1}{0.5} + \frac{1}{2} \]

Calculating the right-hand side:

\[ \frac{1}{R_{\text{eq}}} = 2 + 0.5 = 2.5 \]

Now, taking the reciprocal to find R_eq:

\[ R_{\text{eq}} = \frac{1}{2.5} = 0.4 \, \Omega \]

### Step 4: Calculate the total current through the circuit
The total current flowing through the circuit remains the same as measured, which is 10 A.

### Step 5: Use the current division rule to find the current through the 2 Ω resistor
According to the current division rule, the current through the 2 Ω resistor (I_2) can be calculated as:

\[ I_2 = I \cdot \frac{R_{\text{internal}}}{R_{\text{internal}} + R_{\text{external}}} \]

Substituting the values we have:

\[ I_2 = 10 \, \text{A} \cdot \frac{0.5 \, \Omega}{0.5 \, \Omega + 2 \, \Omega} \]

Calculating the denominator:

\[ I_2 = 10 \, \text{A} \cdot \frac{0.5}{2.5} = 10 \, \text{A} \cdot 0.2 = 2 \, \text{A} \]

### Final Answer
The current flowing through the 2 Ω resistor is **2 A**.

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