of the lamp:\n- Potential difference (pd), $V = 8.4\\text{ V}$\n- Power, $P = 5.6\\text{ W}$\n\nWe need to show that the lamp's resistance, $R$, under these conditions is $12.6\\ \\Omega$.","highlights":[{"text":"8.4 V, 5.6 W","location":"specification"},{"text":"12.6 \\Omega","location":"specification"}]},{"type":"text","order":1,"title":"Calculate the operating current","content":"First, we find the current $I$ flowing through the lamp using the power formula from our electricity studies:\n\n$$P = I \\times V$$\n\nRearranging this to solve for current $I$ gives:\n\n$$I = \\frac{P}{V}$$\n\nSubstituting our given values:\n\n$$I = \\frac{5.6\\text{ W}}{8.4\\text{ V}} = \\frac{2}{3}\\text{ A} \\approx 0.667\\text{ A}$$"},{"type":"text","order":2,"title":"Calculate the resistance","content":"Next, we use Ohm's law to determine the resistance $R$ of the lamp. Ohm's law relates potential difference, current, and resistance:\n\n$$V = I \\times R$$\n\nRearranging to solve for resistance $R$:\n\n$$R = \\frac{V}{I}$$\n\nSubstituting the values we have:\n\n$$R = \\frac{8.4\\text{ V}}{\\frac{2}{3}\\text{ A}} = 8.4 \\times 1.5 = 12.6\\ \\Omega$$\n\nThis confirms the resistance of the lamp is indeed $12.6\\ \\Omega$."}]}],"generatedAt":"2026-06-09T15:19:52.167Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"options":[]},{"id":"c467e982-b5ad-4262-ba1a-d14bcfbf2e45","label":"2","content":"When the lamp is operating at its working pd, the terminal pd across the battery is \$8.4\\text{ V}\$. Calculate the electromotive force (emf) of the battery. Give your answer to 3 significant figures.","markscheme":"- Calculates current through the lamp: $I_{\\text{lamp}} = \\frac{5.6}{8.4} \\approx 0.667\\text{ A}$ B1\n- Calculates current through the $15\\ \\Omega$ resistor: $I_{\\text{resistor}} = \\frac{8.4}{15} = 0.56\\text{ A}$ B1\n- Sums these currents to find total current: $I_{\\text{total}} = 1.227\\text{ A}$ M1\n- Uses $\\varepsilon = V_{\\text{terminal}} + I_{\\text{total}} r$ to obtain $\\varepsilon = 8.4 + (1.227 \\times 1.8) = 10.6\\text{ V}$ A1","marks":4,"order":1,"markingRubric":null,"explanation":{"methods":[{"id":"branchcurrents","label":"Branch Currents Method","steps":[{"type":"text","order":0,"title":"Analyze the given values","content":"Let's first identify the given values from the circuit diagram and text:\n- Resistance of the resistor, $R = 15\\ \\Omega$\n- Lamp rating: $8.4\\text{ V}, 5.6\\text{ W}$\n- Internal resistance of the battery, $r = 1.8\\ \\Omega$\n- Terminal potential difference, $V = 8.4\\text{ V}$\n\nSince the parallel network is connected across the battery, the potential difference across both the resistor branch and the lamp branch is equal to the terminal pd of the battery, which is $V = 8.4\\text{ V}$.","highlights":[{"text":"15 ohms","location":"specification"},{"text":"8.4 V, 5.6 W","location":"specification"},{"text":"1.8","location":"specification"},{"text":"8.4 V","location":"specification"}]},{"type":"text","order":1,"title":"Calculate lamp current","content":"To find the current flowing through the lamp branch ($I_{\\text{lamp}}$), we use the power formula from the data booklet:\n\n$$P = I \\times V$$\n\nRearranging for current:\n\n$$I_{\\text{lamp}} = \\frac{P_{\\text{lamp}}}{V}$$\n\nSubstituting our known values:\n\n$$I_{\\text{lamp}} = \\frac{5.6\\text{ W}}{8.4\\text{ V}} \\approx 0.667\\text{ A}$$\n\n*(This calculation earns you the first mark B1)*"},{"type":"text","order":2,"title":"Calculate resistor current","content":"Next, we calculate the current flowing through the $15\\ \\Omega$ resistor branch ($I_{\\text{resistor}}$) using Ohm's law:\n\n$$I_{\\text{resistor}} = \\frac{V}{R}$$\n\nSubstituting our known values:\n\n$$I_{\\text{resistor}} = \\frac{8.4\\text{ V}}{15\\ \\Omega} = 0.56\\text{ A}$$\n\n*(This calculation earns you the second mark B1)*"},{"type":"text","order":3,"title":"Calculate total current","content":"According to Kirchhoff's First Law, the total current ($I_{\\text

Current electricity

Question 51

Current electricity Questions

Current electricity

Question 51

Current electricity Questions