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
Step 1: Define EMF. Electromotive force (EMF) is the maximum potential difference that a battery or source of electrical energy 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 source. Step 2: Explain why the voltmeter reading decreases. When the switch S is closed, current flows through the external circuit. This current also flows through the internal resistance (r) of the battery, causing a potential drop (Ir) across the internal resistance. The voltmeter measures the terminal potential difference (V_terminal), which is given by V_terminal = - Ir. Since Ir > 0 when current flows, the terminal potential difference is less than the EMF, causing the voltmeter reading to decrease. Step 3: Calculate the total external resistance. Resistors R_2 and R_3 are in parallel. Their equivalent resistance (R_p) is: (1)/(R_p) = (1)/(R_2) + (1)/(R_3) (1)/(R_p) = (1)/(25 \, ) + (1)/(15 \, ) (1)/(R_p) = (3)/(75 \, ) + (5)/(75 \, ) = (8)/(75 \, ) R_p = (75)/(8) \, = 9.375 \, Resistor R_1 is in series with R_p. The total external resistance (R_ext) is: R_ext = R_1 + R_p R_ext = 4 \, + 9.375 \, R_ext = 13.375 \, Step 4: Calculate the reading on the ammeter. The decrease in voltmeter reading (1.5 \, V) is due to the potential drop across the internal resistance (Ir). Ir = 1.5 \, V Given the internal resistance r = 0.5 \, : I (0.5 \, ) = 1.5 \, V I = 1.5 \, V0.5 \, I = 3 \, A Step 5: Calculate the EMF of the battery. The EMF () is given by the formula = I(R_ext + r). = 3 \, A (13.375 \, + 0.5 \, ) = 3 \, A (13.875 \, ) = 41.625 \, V Step 6: Evaluate the statement about current through R_2 and R_3. The statement is: "The current through resistor R_3 is larger than the current through resistor R_2." Resistors R_2 (25 \, ) and R_3 (15 \, ) are connected in parallel, meaning the voltage across them is the same. According to Ohm's Law (I = V/R), current is inversely proportional to resistance. Since R_3 < R_2, the current through R_3 will be greater than the current through R_2. Therefore, the statement is CORRECT. Step 7: Determine the effect of removing R_1 on the EMF. The EMF of a battery is an intrinsic property of the battery itself, determined by its chemical composition and internal structure. It represents the maximum potential difference the battery can provide. Removing an external resistor changes the total external resistance of the circuit, which affects the total current and the terminal potential difference, but it does not change the fundamental EMF of the battery. Therefore, the EMF of the battery REMAINS THE SAME. Send me the next one 📸