Answer:
[tex]R_{eq} = 30.6\,\Omega[/tex]
Explanation:
The equivalent resistance formulas are:
[tex]R_S = R_1 + R_2 + R_3 + ...[/tex]
[tex]R_P = \dfrac{1}{\dfrac{1}{R_1}+\dfrac{1}{R_2}+...}[/tex]
for resistors in series and in parallel.
First, we can get the equivalent resistance of the parallel resistors:
[tex]R_P = \dfrac{1}{\dfrac{1}{36\,\Omega} + \dfrac{1}{4\,\Omega}}[/tex]
[tex]R_P = 3.6\,\Omega[/tex]
Then, we can input this into the series equation to get the total equivalent resistance of the circuit:
[tex]R_{eq} = 3.6\,\Omega + 27\,\Omega[/tex]
[tex]R_{eq} = 30.6\,\Omega[/tex]
Further Note
We can solve for the current through the single-wire (non-parallel) parts of the circuit using the equation:
[tex]I=\dfrac{\Delta V}{R}[/tex]
where:
- [tex]I=\text{current}[/tex]
- [tex]\Delta V=\text{voltage drop}[/tex]
- [tex]R=\text{resistance}[/tex]
Plugging in the known values, we get:
[tex]I=\dfrac{40\text{ V}}{30.3\,\Omega} = 1.31\text{ A}[/tex]
