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NEETPhysicsAlternating Current

Match the following ( array |c|l|c|l| & Currents & & r.m.s. values (1) & x₀ t & (i) & x₀ (2) & x₀ t t & (ii) & x₀ 2 (3) & x₀ t + x₀ t & (iii) & x₀ 2 2 array )

Options

  1. A1 (i),2 (ii),3 (iii)
  2. B1 (ii), 2 (iii),3 (i)
  3. C1 (i),2 (iii),3 (ii)
  4. DNone of these

Correct answer

B. 1 (ii), 2 (iii),3 (i)

Step-by-step solution

1. (x₀ ( t) ) : This is a pure sinusoidal function. The r.m.s. value of a sinusoidal function (A ( t) ) is (A / 2 ). So, the r.m.s. value of (x₀ ( t) ) is (x₀ / 2 ). 2. (x₀ ( t) ( t) ) : Using the trigonometric identity ( (2 t)=2 ( t) ( t) ), this can be rewritten as ( x₀ 2 (2 t) ), which is again a sinusoidal function. The r.m.s. value will be ( x₀ 2 2 ). 3. (x₀ ( t)+x₀ ( t) ) : This is a sum of two sinusoidal functions. The r.m.s. value of such a sum can befound by using 2 r.m.s. (= ( x₀ 2 )^2+ ( x₀ 2 )^2 = ). No

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