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
Here are the solutions to your problems. Problem 1 (Power wasted in a cable): Calculate the power wasted through a cable of resistance 0.5 \, when 11 \, kW electricity generated is transmitted through it at 120 \, V. Step 1: Identify the given values. Resistance of the cable (R) = 0.5 \, . Electricity generated (P_gen) = 11 \, kW = 11000 \, W. Transmission voltage (V) = 120 \, V. Step 2: Calculate the current flowing through the cable during transmission. The current (I) can be found using the formula P = V I. I = P_genV I = 11000 \, W120 \, V I ≈ 91.6667 \, A Step 3: Calculate the power wasted in the cable. The power wasted (P_wasted) due to the resistance of the cable is given by P_wasted = I^2 R. P_wasted = (91.6667 \, A)^2 × 0.5 \, P_wasted = 8402.78 × 0.5 \, W P_wasted = 4201.39 \, W To express in kilowatts: P_wasted = (4201.39)/(1000) \, kW P_wasted ≈ 4.20 \, kW The power wasted in the cable is 4.20 kW. Note: The provided answer in the image (1.05 KW) does not match the calculation based on the given values. Problem 2 (Resonance frequency): A 10 \, mF capacitor is connected in series with a coil of 2 \, mH inductance and 5.0 \, resistance. Determine the resonance frequency. Step 1: Identify the given values. Capacitance (C) = 10 \, mF = 10 × 10^-3 \, F. Inductance (L) = 2 \, mH = 2 × 10^-3 \, H. Resistance (R) = 5.0 \, . (Note: Resistance does not affect the resonance frequency itself in a series RLC circuit). Step 2: Use the formula for resonance frequency (f_0) in a series RLC circuit. f_0 = (1)/(2(LC)) Step 3: Substitute the values and calculate the resonance frequency. f_0 = (1)/(2((2 × 10^-3) \, H))(10 × 10^-3 \, F) f_0 = (1)/(2(20 × 10^-6) \, H) · F f_0 = (1)/(2 × sqrt(20) × 10^-3) f_0 =