![A radio signal of length L, emits a signal of wavelength λ and power P. These equation quantities are related by P = K I² [L/λ]² where I is current. Determine the S.I unit of K](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1781676395526-66515af225d1e31f.png&w=3840&q=75)
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 SI unit of K, we need to analyze the given equation and the SI units of each variable. The given equation is: P = KI^2 [(L)/()]^2 Step 1: Identify the SI units of the known quantities. • P (Power) has the SI unit of Watt (W). • I (Current) has the SI unit of Ampere (A). • L (Length) has the SI unit of meter (m). • (Wavelength) has the SI unit of meter (m). Step 2: Substitute the units into the equation. We want to find the unit of K. Let [X] denote the unit of quantity X. [P] = [K] [I]^2 [(L)/()]^2 Substitute the known units: W = [K] (A)^2 [mm]^2 Step 3: Simplify the units. The term [mm]^2 simplifies to (1)^2 = 1, as it is a ratio of two lengths, making it dimensionless. So the equation becomes: W = [K] · A^2 · 1 W = [K] · A^2 Step 4: Solve for the unit of K. Divide both sides by A^2: [K] = WA^2 The SI unit of K is WA^2. Alternatively, we can express this in terms of base SI units: Since 1 W = 1 Js and 1 J = 1 N · m = 1 kg · ms^2 · m = 1 kg · m^2s^2, Then 1 W = 1 kg · m^2s^3. So, the unit of K can also be expressed as: [K] = kg · m^2/s^3A^2 = kg · m^2 · s^-3 · A^-2 Drop the next question.