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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Hey CØTBØJ, good to see you again. Let's break down electromagnetic induction and transformers. Electromagnetic Induction & Average Induced EMF Electromagnetic induction is the process where a conductor placed in a changing magnetic field (or a conductor moving through a magnetic field) has an electromotive force (EMF) induced across it. If the conductor forms a closed circuit, this induced EMF drives an induced current. The magnitude of the induced EMF is given by Faraday's Law of Induction: EMF = -N (ΔΦ)/(Δt) Where: EMF is the induced electromotive force (in Volts, V). N is the number of turns in the coil. ΔΦ is the change in magnetic flux (in Weber, Wb). Magnetic flux (Φ) is the product of the magnetic field strength (B) and the area (A) perpendicular to the field: Φ = B × A. Δt is the time interval over which the flux changes (in seconds, s). The negative sign indicates the direction of the induced EMF (Lenz's Law), opposing the change in magnetic flux. For calculations of magnitude, we often use the absolute value. This formula directly calculates the average induced EMF over the time interval Δt. Example Calculation: A coil with 100 turns has its magnetic flux change from 0.05 Wb to 0.01 Wb in 0.2 seconds. Step 1: Identify the given values. N = 100 turns ΔΦ = Φ_final - Φ_initial = 0.01 Wb - 0.05 Wb = -0.04 Wb Δt = 0.2 s Step 2: Apply Faraday's Law. EMF = -N (ΔΦ)/(Δt) EMF = -100 × (-0.04 Wb)/(0.2 s) EMF = -100 × (-0.2 V) EMF = 20 V Transformers A transformer is a device that changes AC voltage from one level to another using electromagnetic induction. It consists of two coils, a primary coil (input) and a secondary coil (output), wound around a common soft iron core. 1. Voltage and Turns Ratio: For an ideal transformer, the ratio of the voltages is directly proportional to the ratio of the number of turns in the coils: V_p / V_s = N_p / N_s Where: V_p is the voltage across the primary coil. V_s is the voltage across the secondary coil. N_p is the number of turns in the primary coil. N_s is the number of turns in the secondary coil. Example Calculation: A transformer has 200 turns in its primary coil and 50 turns in its secondary coil. If the primary voltage is 120 V, what is the secondary voltage? Step 1: Identify the given values. N_p = 200 turns N_s = 50 turns V_p = 120 V Step 2: Apply the voltage and turns ratio formula. V_p / V_s = N_p / N_s 120 V / V_s = 200 / 50 120 V / V_s = 4 Step 3: Solve for V_s. V_s = 120 V / 4 V_s = 30 V 2. Current in Transformers: For an ideal transformer, power is conserved (input power equals output power). P_p = P_s V_p I_p = V_s I_s From this, we can derive the current ratio: I_p / I_s = V_s / V_p = N_s / N_p This shows that current is inversely proportional to voltage and the number of turns. If voltage steps up, current steps down, and vice versa. Example Calculation (using previous example): If the primary current in the transformer above is 0.5 A, what is the secondary current? Step 1: Identify the given values. V_p = 120 V I_p = 0.5 A V_s = 30 V (from previous calculation) Step 2: Apply the power conservation formula. V_p I_p = V_s I_s 120 V × 0.5 A = 30 V × I_s 60 W = 30 V × I_s Step 3: Solve for I_s. I_s = 60 W / 30 V I_s = 2 A 3. Efficiency of Transformer: Real transformers are not 100% efficient due to energy losses (e.g., heat loss in coils, eddy currents in the core, magnetic flux leakage). The efficiency (η) is the ratio of output power to input power, usually expressed as a percentage: η = (P_out)/(P_in) × 100% Where: P_out is the output power (V_s I_s). P_in is the input power (V_p I_p). Example Calculation: A transformer has an input power of 100 W and an output power of 95 W. What is its efficiency? Step 1: Identify the given values. P_in = 100 W P_out = 95 W Step 2: Apply the efficiency formula. η = (P_out)/(P_in) × 100% η = (95 W)/(100 W) × 100% η = 0.95 × 100% η = 95% What's next? Send 'em 📸