This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
8.1 Define the term emf of a battery. The electromotive force (EMF) of a battery is the maximum potential difference that the battery can provide across its terminals when no current is flowing in the external circuit. It represents the total energy supplied per unit charge by the battery. 8.2 Give a reason why the voltmeter reading decreases. When switch S is closed, the total external resistance of the circuit increases because the parallel combination of R_2 and R_3 is added in series with R_1. An increase in total external resistance leads to a decrease in the total current flowing from the battery. Since the voltmeter measures the voltage across R_1 (V_R1 = I × R_1), and R_1 is constant, a decrease in the total current I results in a decrease in the voltmeter reading. 8.3 Calculate the following when switch S is closed: 8.3.3 Emf (E) of the battery Step 1: Calculate the total external resistance when switch S is open. When S is open, only R_1 is in the external circuit. R_ext, open = R_1 = 4 \, The total resistance of the circuit is R_total, open = R_ext, open + r = 4 \, + 0.5 \, = 4.5 \, . The current flowing is I_open = ER_total, open = E4.5. The voltmeter measures the voltage across R_1: V_R1, open = I_open R_1 = E4.5 × 4 = (8)/(9)E Step 2: Calculate the total external resistance when switch S is closed. When S is closed, R_2 and R_3 are in parallel. R_p = ((1)/(R_2) + (1)/(R_3))^-1 = ((1)/(25 \, ) + (1)/(15 \, ))^-1 R_p = ((3+5)/(75))^-1 = ((8)/(75))^-1 = (75)/(8) \, = 9.375 \, The total external resistance is R_ext, closed = R_1 + R_p = 4 \, + 9.375 \, = 13.375 \, . The total resistance of the circuit is R_total, closed = R_ext, closed + r = 13.375 \, + 0.5 \, = 13.875 \, . The current flowing is I_closed = ER_total, closed = E13.875. The voltmeter measures the voltage across R_1: V_R1, closed = I_closed R_1 = E13.875 × 4 = (32)/(111)E Step 3: Use the given information that the voltmeter reading decreases by 1.5 V. V_R1, open - V_R1, closed = 1.5 \, V (8)/(9)E - (32)/(111)E = 1.5 E ((8)/(9) - (32)/(111)) = 1.5 E ((8 × 37 - 32 × 3)/(333)) = 1.5 E ((296 - 96)/(333)) = 1.5 E ((200)/(333)) = 1.5 E = 1.5 × (333)/(200) = (3)/(2) × (333)/(200) = (999)/(400) E = 2.4975 \, V The EMF of the battery is 2.50 V. 8.3.2 Total external resistance of the circuit Step 1: Calculate the equivalent resistance of the parallel combination of R_2 and R_3. R_p = ((1)/(25 \, ) + (1)/(15 \, ))^-1 = 9.375 \, Step 2: Calculate the total external resistance when switch S is closed. R_ext, closed = R_1 + R_p R_ext, closed = 4 \, + 9.375 \, R_ext, closed = 13.375 \, The total external resistance of the circuit is 13.38 . 8.3.1 Reading on the ammeter Step 1: Calculate the total current flowing when switch S is closed. The ammeter measures the total current I_closed. I_closed = ER_ext, closed + r I_closed = (2.4975 \, V)/(13.375 \, + 0.5 \, ) I_closed = (2.4975 \, V)/(13.875 \, ) I_closed ≈ 0.180 \, A The reading on the ammeter is 0.18 A. 8.4 A learner makes the following statement: The current through resistor R_3 is larger than the current through resistor R_2. Is this statement CORRECT? Choose from YES or NO. Explain the answer. YES Explanation: Resistors R_2 and R_3 are connected in parallel, meaning the potential difference across them is the same. According to Ohm's Law (I = V/R), for a constant voltage, the current is inversely proportional to the resistance. Since R_3 (15 \, ) is smaller than R_2 (25 \, ), the current through R_3 will be larger than the current through R_2. 8.5 The 4 resistor is now removed from the circuit. How will this affect the emf of the battery? Choose from INCREASES, DECREASES or REMAINS THE SAME. REMAINS THE SAME Explanation: The electromotive force (EMF) of a battery is an intrinsic property of the battery itself, determined by its chemical composition. It does not depend on the external circuit connected to it. Removing a resistor from the external circuit will change the external resistance, current, and terminal potential difference, but not the EMF. That's 2 down. 3 left today — send the next one.