Let's break down and explain each step from the solution in the image: --- ### **Step 1: Finding the Magnitude of the Current** **Formula Used:** \[ P = V \cdot I \] Where: - \( P \) = Power (in Watts, W) - \( V \) = Voltage (in Volts, V) - \( I \) = Current (in Amperes, A) **Rearrange to find current:** \[ I = \frac{P}{V} \] **Substitute the values:** - \( P = 150\, \text{W} \) - \( V = 10\, \text{V} \) \[ I = \frac{150\, \text{W}}{10\, \text{V}} = 15\, \text{A} \] --- ### **Step 2: Finding the Kettle's Resistance** **Formula Used:** \[ V = I \cdot R \] Where: - \( R \) = Resistance (in Ohms, Ω) **Rearrange to find resistance:** \[ R = \frac{V}{I} \] **Substitute the values:** - \( V = 10\, \text{V} \) - \( I = 15\, \text{A} \) \[ R = \frac{10\, \text{V}}{15\, \text{A}} = \frac{2}{3}\, \Omega = 0.67\, \Omega \] --- ### **Step 3: Finding the Battery Capacity Required** #### **(a) In Joules (J) or Kilojoules (kJ):** **Formula Used:** \[ E = P \cdot t \] Where: - \( E \) = Energy (in Joules, J) - \( t \) = Time (in seconds, s) **Convert time:** - \( 30\, \text{minutes} = 30 \times 60 = 1800\, \text{seconds} \) **Substitute the values:** - \( P = 150\, \text{W} \) - \( t = 1800\, \text{s} \) \[ E = 150\, \text{W} \times 1800\, \text{s} = 270,000\, \text{J} = 270\, \text{kJ} \] (\( 1\, \text{kJ} = 1000\, \text{J} \)) --- #### **(b) In Watt-hours (Wh):** **Convert time:** - \( 30\, \text{minutes} = 0.5\, \text{hours} \) **Substitute the values:** - \( P = 150\, \text{W} \) - \( t = 0.5\, \text{h} \) \[ E = 150\, \text{W} \times 0.5\, \text{h} = 75\, \text{Wh} \] --- ### **Final Answer** **The battery needs a minimum capacity of 75 Wh or 270 kJ to run the kettle for 30 minutes.** --- ## **Explanation of Terms:** - **Power (P):** The rate at which energy is used or produced, measured in Watts (W). - **Voltage (V):** The potential difference or 'pressure' that pushes electric current around a circuit, measured in Volts (V). - **Current (I):** The flow of electric charge, measured in Amperes (A). - **Resistance (R):** The opposition that a substance offers to the flow of electric current, measured in Ohms (Ω). - **Energy (E):** The capacity to do work, measured in Joules (J), kilojoules (kJ), or Watt-hours (Wh). - **Time (t):** The duration for which the device operates, measured in seconds (s) or hours (h). --- **Summary:** To operate the kettle for 30 minutes, your battery should be able to supply at least **75 Wh** or **270 kJ** of energy.