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.
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For a parallel circuit, the voltage across each component is the same as the total voltage. Step 1: Determine voltages across resistors. The total voltage E_T is given as 9V. In a parallel circuit, the voltage across each resistor is equal to the total voltage. V_1 = V_2 = E_T = 9V Step 2: Calculate currents through each resistor. We use Ohm's Law, I = (V)/(R). Given R_1 = 1k = 1000 and R_2 = 10k = 10000. I_1 = (V_1)/(R_1) = (9V)/(1000) = 0.009A = 9mA I_2 = (V_2)/(R_2) = (9V)/(10000) = 0.0009A = 0.9mA Step 3: Calculate total current. The total current in a parallel circuit is the sum of the individual branch currents. I_T = I_1 + I_2 = 0.009A + 0.0009A = 0.0099A = 9.9mA Step 4: Calculate power dissipated by each resistor. We use the power formula, P = V · I. P_1 = V_1 · I_1 = 9V · 0.009A = 0.081W = 81mW P_2 = V_2 · I_2 = 9V · 0.0009A = 0.0081W = 8.1mW Step 5: Calculate total power. The total power is the sum of the power dissipated by each resistor. P_T = P_1 + P_2 = 0.081W + 0.0081W = 0.0891W = 89.1mW Alternatively, P_T = E_T · I_T = 9V · 0.0099A = 0.0891W. Step 6: Calculate total resistance. For parallel resistors, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances. (1)/(R_T) = (1)/(R_1) + (1)/(R_2) = (1)/(1000) + (1)/(10000) (1)/(R_T) = (10)/(10000) + (1)/(10000) = (11)/(10000) R_T = (10000)/(11) ≈ 909.09 = 0.909k Step 7: Enter the values into the table. The completed table is: | | VCE (V) | I (mA) | R (k) | P (mW) | |---|---|---|---|---| | R_1 | 9 | 9 | 1 | 81 | | R_2 | 9 | 0.9 | 10 | 8.1 | | Total | 9 | 9.9 | 0.909 | 89.1 | The unknown values are: V_1 = 9 V I_1 = 9 mA P_1 = 81 mW V_2 = 9 V I_2 = 0.9 mA P_2 = 8.1 mW I_T = 9.9 mA R_T = 0.909 k P_T = 89.1 mW Send me the next one 📸