The potential difference across terminals of cell of 20 V and `r = 2 Omega` connected to `8 Omega` external resistance is

Options

A. 16
B. 1.6
C. 160
D. 5

Explanation

To find the potential difference across the terminals of a cell with an EMF of 20 V and an internal resistance of 2 Ω connected to an external resistance of 8 Ω, we can follow these steps:

### Step 1: Identify the total resistance in the circuit
The total resistance (R_total) in the circuit is the sum of the internal resistance (r) and the external resistance (R_ext):
\[ R_{\text{total}} = r + R_{\text{ext}} = 2 \, \Omega + 8 \, \Omega = 10 \, \Omega \]

**Hint:** Remember that in a series circuit, resistances simply add up.

### Step 2: Calculate the current flowing through the circuit
Using Ohm's Law, we can find the current (I) flowing through the circuit:
\[ I = \frac{V}{R_{\text{total}}} = \frac{20 \, V}{10 \, \Omega} = 2 \, A \]

**Hint:** Ohm's Law states that \( V = IR \). Rearranging gives you the current when you know the voltage and resistance.

### Step 3: Calculate the potential drop across the internal resistance
The potential drop (V_drop) across the internal resistance can be calculated using:
\[ V_{\text{drop}} = I \times r = 2 \, A \times 2 \, \Omega = 4 \, V \]

**Hint:** The potential drop across a resistor in a circuit can be calculated using the formula \( V = IR \).

### Step 4: Calculate the potential difference across the terminals of the cell
The potential difference (V_AB) across the terminals of the cell is given by:
\[ V_{AB} = V_{\text{EMF}} - V_{\text{drop}} = 20 \, V - 4 \, V = 16 \, V \]

**Hint:** The potential difference across the terminals is the EMF minus the voltage drop across the internal resistance.

### Final Answer:
The potential difference across the terminals of the cell is **16 V**.