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The potential difference V and the current I flowing through an instrument in an A.C. circuit of frequency f are given by V = 5 cos ωt volts and I = 2 sin ωt amperes (where ω = 2πf). The power dissipated in the instrument is
  • a)
    Zero
  • b)
    10 watts
  • c)
    5 watts
  • d)
    2.5 watts
Correct answer is option 'A'. Can you explain this answer?
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Given Parameters:
The potential difference V = 5 cos ωt volts and the current I = 2 sin ωt amperes in an A.C. circuit of frequency f.

Calculation of Power Dissipated:
- In an A.C. circuit, the power dissipated is given by P = VIcosΦ, where Φ is the phase difference between V and I.
- Here, V = 5 cos ωt and I = 2 sin ωt.
- The phase difference between cos ωt and sin ωt is π/2.
- Therefore, cosΦ = cos(π/2) = 0.
- Hence, the power dissipated in the instrument is P = 5 * 2 * 0 = 0 watts.

Conclusion:
- The power dissipated in the instrument is zero.
- This indicates that the instrument is purely capacitive or inductive, where the power is alternately absorbed and returned to the circuit, resulting in no net power dissipation.
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The potential difference V and the current I flowing through an instrument in an A.C. circuit of frequency f are given by V = 5 cos ωt volts and I = 2 sin ωt amperes (where ω = 2πf). The power dissipated in the instrument isa)Zerob)10 wattsc)5 wattsd)2.5 wattsCorrect answer is option 'A'. Can you explain this answer?
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