Resistance of the Network:
The resistor network consists of:
One resistor \(R\) in series with two resistors \(R\) and \(R\) in parallel.
Step 1: Equivalent resistance of the parallel resistors
The formula for the equivalent resistance \(R_{\text{parallel}}\) of two resistors \(R_1\) and \(R_2\) in parallel is:
\[\frac{1}{R_{\text{parallel}}} = \frac{1}{R_1} + \frac{1}{R_2}\]
Here, \(R_1 = R\) and \(R_2 = R\). Therefore:
\[\frac{1}{R_{\text{parallel}}} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R}\]
\[R_{\text{parallel}} = \frac{R}{2}\]
Step 2: Total resistance of the network
The equivalent resistance \(R_{\text{total}}\) is the series combination of the first resistor \(R\) and the parallel equivalent resistance \(R_{\text{parallel}}\):
\[R_{\text{total}} = R + R_{\text{parallel}}\]
Substitute \(R_{\text{parallel}} = \frac{R}{2}\):
\[R_{\text{total}} = R + \frac{R}{2}\]
\[R_{\text{total}} = \frac{2R}{2} + \frac{R}{2} = \frac{3R}{2}\]
Final Answer: The total resistance of the network is:
\[R_{\text{total}} = \frac{3R}{2}.\]
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Proteins control the expression of various characters. Explain this statement by taking an example of "tallness" as a characteristic in plants
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