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
To determine the active power in the circuit, we need to calculate the impedance, current, and then apply the power formula. Step 1: Calculate the impedance (Z) of the coil. The impedance of a series RL circuit is given by Z = R + jX_L. Z = 12 \, + j12 \, To convert this to polar form, we find the magnitude |Z| and phase angle _Z. |Z| = sqrt(R^2 + X_L^2) = sqrt(12^2 + 12^2) = sqrt(144 + 144) = sqrt(288) = 12sqrt(2) \, _Z = ((X_L)/(R)) = ((12)/(12)) = (1) = 45^ So, the impedance is Z = 12sqrt(2) 45^ \, . Step 2: Calculate the current (I) flowing through the circuit. Using Ohm's Law for AC circuits, I = (V)/(Z). Given V = 52 30^ \, V. I = 52 30^ \, V12sqrt(2) 45^ \, |I| = (52)/(12sqrt(2)) = (13)/(3sqrt(2)) = 13sqrt(2)6 \, A _I = 30^ - 45^ = -15^ So, the current is I = 13sqrt(2)6 -15^ \, A. Step 3: Calculate the active power (P). Active power can be calculated using the formula P = |I|^2 R, where |I| is the magnitude of the current and R is the resistance. P = (13sqrt(2)6)^2 × 12 \, P = ((169 × 2)/(36)) × 12 P = ((169)/(18)) × 12 P = (169 × 12)/(18) = (169 × 2)/(3) = (338)/(3) \, W P ≈ 112.67 \, W The active power in the circuit is 112.67 W. Send me the next one 📸