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
let's re-examine the calculation for question 1.2. The previous solution was correct, but I'll present it again with all the steps for clarity. QUESTION 1 1.2 Study FIGURE 2 below. Using Thevenin's method, calculate the current flowing through the 15 resistor. Step 1: Remove the 15 resistor (R_5) and find V_Th (Thevenin voltage across terminals B and D). We need to find the potential difference between points B and D. Let's assume point C is the reference ground (0 V). The voltage at point A is V_T = 5 V. The voltage at point B (V_B) can be found using the voltage divider rule for the series combination of R_2 and R_3 connected across V_T: V_B = V_T × (R_3)/(R_2 + R_3) = 5 V × (5 )/(35 + 5 ) = 5 V × (5)/(40) = 0.625 V The voltage at point D (V_D) can be found using the voltage divider rule for the series combination of R_1 and R_4 connected across V_T: V_D = V_T × (R_4)/(R_1 + R_4) = 5 V × (10 )/(30 + 10 ) = 5 V × (10)/(40) = 1.25 V The Thevenin voltage V_Th is the potential difference between D and B: V_Th = V_D - V_B = 1.25 V - 0.625 V = 0.625 V Step 2: Find R_Th (Thevenin resistance looking into terminals B and D). To find R_Th, we turn off the independent voltage source (V_T = 0 V), which means we replace it with a short circuit. This connects points A and C together. Now, looking into terminals B and D: From terminal B, resistors R_2 (35 ) and R_3 (5 ) are connected between B and the shorted A-C line. Therefore, R_2 and R_3 are in parallel: R_B,eq = R_2 || R_3 = (35 × 5 )/(35 + 5 ) = (175)/(40) = 4.375 From terminal D, resistors R_1 (30 ) and R_4 (10 ) are connected between D and the shorted A-C line. Therefore, R_1 and R_4 are in parallel: R_D,eq = R_1 || R_4 = (30 × 10 )/(30 + 10 ) = (300)/(40) = 7.5 The Thevenin resistance R_Th is the series combination of R_B,eq and R_D,eq because they are connected end-to-end between terminals B and D: R_Th = R_B,eq + R_D,eq = 4.375 + 7.5 = 11.875 Step 3: Calculate the current flowing through the 15 resistor (R_5). Now, we connect the 15 resistor (R_5) to the Thevenin equivalent circuit (a voltage source V_Th in series with R_Th). The current I_R5 flowing through R_5 is given by Ohm's Law: I_R5 = V_ThR_Th + R_5 = 0.625 V11.875 + 15 = 0.625 V26.875 I_R5 ≈ 0.0232558 A The current flowing through the 15 resistor is 0.0233 A. What's next?