Answer:
7086.16 s Here, \[{{E}_{V}}=10\,V,\] \[\text{v}=650\,Hz,\] \[R=100\Omega ,\] \[C=10\mu F=10\times {{10}^{-6}}F,\]\[L=0.15H,\]\[\Delta \theta =10{}^\circ C,\] \[ms=20\text{J}{}^\circ \text{/C}\] As,\[{{X}_{L}}=2\pi \,\text{v}L=2\times \frac{22}{7}\times 650\times 0.15=612.61\Omega \] And \[{{X}_{C}}=\frac{1}{2\pi \,\text{v}C}\] \[=\frac{1}{2\times \frac{22}{7}\times 650\times 10\times {{10}^{-6}}}=24.48\,\Omega \] \[Z=\sqrt{{{R}^{2}}+{{({{X}_{L}}-{{X}_{C}})}^{2}}}\] \[=\sqrt{{{(100)}^{2}}+{{(612.61-24.48)}^{2}}}\] \[=596.57\,\Omega \]\[{{I}_{V}}=\frac{{{E}_{V}}}{Z}=\frac{10}{596.57}=0.0168\] As, \[I_{V}^{2}\,Rt=(ms)\,\Delta \theta \] \[\therefore \]\[t=\frac{(ms)\,\Delta \theta }{I_{V}^{2}R}=\frac{20\times 10}{{{(0.0168)}^{2}}\times 100}=7086.16\,s\]
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