Question

According to the Laws of Proportionality, if a resistor in a parallel circuit has twice the resistance of a second resistor, it will have _______________ the current of the second resistor.

Answer 1

Answer:

When a resistor in a parallel circuit has twice the resistance of a second resistor, then the resistor has half the current of the second resistor.

Explanation:

It is given that the parallel circuit has two resistors. One is twice the second resistor. It is required to find the current in the first resistor in terms of the second resistor.

Let us consider R and S are in parallel and the potential difference is V on each of the resistors.

If the source current is I, then, the current through the resistor R is,

$I_R=\frac{S}{R+S}\times I$

And similarly, the current through the resistor S is,

$I_S=\frac{R}{R+S}\times I$

Therefore, the ratio of the currents is,

$\begin{aligned}\frac{I_R}{I_S}&=\frac{\frac{S}{R+S}\times I}{\frac{R}{R+S}\times I}\\&=\frac{S}{R}\end{aligned}$

Here, let, the second resistor is, S=r, then the first resistor, R=2r.

Therefore,

$\begin{aligned}\frac{I_R}{I_S}&=\frac{r}{2r}\\\rightarrow I_R&=\frac{1}{2} I_S\end{aligned}$

To know more about the current division in a parallel circuit, refer to:

brainly.com/question/9764589

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