GATE Electronics and Communications (EC) 2019 Solved Paper

Question : 19 of 65

Marks: +1, -0

Radiation resistance of a small dipole current element of length I at a frequency of

3 {GHz}

is 3 ohms. If the length is changed by

1 \%

, then the percentage change in the radiation resistance, rounded off to two decimal places, is

\%

Solution:

R_{\rad}=80 π^{2}(\;{d l}/{λ})^{2}

80 π^{2}(\;{ {d} ∣ {f}}/{ {C}})^{2}

∴ {R}_{ {\rad}} ∝ {I}^{2} f^{2}

Now frequency is constant

∴ {R}_{ {\rad}} ∝ {f}^{2}

∴ \;{∆ {R}}/{ {R}}=2 \;{∆ {l}}/{ {I}}

=2 × 1 \%

∴ \;{∆ {R}}/{ {R}}=2 \%

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