A) 570 \[\Omega \]
B) 600 \[\Omega \]
C) 350 \[\Omega \]
D) 35 \[\Omega \]
Correct Answer: A
Solution :
\[i=\frac{\varepsilon }{{{R}_{A}}+\frac{{{R}_{V}}R}{{{R}_{V}}+R}}\,\,=\,\,\frac{\varepsilon \,({{R}_{V}}+R)}{{{R}_{A}}{{R}_{V}}+{{R}_{A}}R+{{R}_{V}}R}\] \[V=\frac{{{R}_{V}}R\varepsilon }{({{R}_{V}}+R)\left[ {{R}_{A}}+\frac{{{R}_{V}}R}{{{R}_{V}}+R} \right]}\] \[V=\frac{{{R}_{V}}R\varepsilon }{{{R}_{A}}{{R}_{V}}+{{R}_{A}}R+{{R}_{V}}R}\] \[{{R}_{res}}=\,\frac{V}{i}\] \[{{R}_{res}}=\,30-30\times \frac{5}{100}\] \[=\,\,30\left[ 1-\frac{5}{100} \right]\,=\,28.5\] \[28.5\,=\,\frac{{{R}_{V}}R}{{{R}_{V}}+R}\] \[28.5\text{ }{{R}_{V}}+28.5\times 30={{R}_{V}}\times 30\] \[30\times 28.5={{R}_{V}}\times 1.5\] \[{{R}_{V}}=\frac{28.5}{1.5}\,\times 30=570\,\Omega \]You need to login to perform this action.
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