b) The voltage across a battery's terminals before connection to a circuit is 12 V . When it is connected to a \( 115 \Omega \) resistor, it draws a current of 100 mA . Calculate the internal resistance of the battery.

To find the internal resistance of the battery, we can use Ohm's law and the formula for the total voltage in a circuit. 1. **Given Data:** - Voltage across the battery's terminals (open circuit voltage, \( V \)) = 12 V - Resistance of the resistor (\( R \)) = 115 Ω - Current drawn (\( I \)) = 100 mA = 0.1 A 2. **Using Ohm's Law:** The voltage across the resistor can be calculated using Ohm's law: \[ V_R = I \times R \] Substituting the values: \[ V_R = 0.1 \, \text{A} \times 115 \, \Omega = 11.5 \, \text{V} \] 3. **Finding the Internal Resistance:** The total voltage from the battery is equal to the voltage across the resistor plus the voltage drop across the internal resistance (\( r \)) of the battery: \[ V = V_R + V_r \] where \( V_r = I \times r \). Rearranging gives: \[ V_r = V - V_R \] Substituting the known values: \[ V_r = 12 \, \text{V} - 11.5 \, \text{V} = 0.5 \, \text{V} \] 4. **Calculating Internal Resistance:** Now we can find the internal resistance \( r \): \[ V_r = I \times r \implies r = \frac{V_r}{I} \] Substituting the values: \[ r = \frac{0.5 \, \text{V}}{0.1 \, \text{A}} = 5 \, \Omega \] Thus, the internal resistance of the battery is \( \boxed{5 \, \Omega} \).