Question

Please helpppppppppppp - question: what is the equivalent resistance of the resistors in the circuit (AC power supply) as shown?

Answer 1

We will have the following:

We will first find the equivalent resistances of each parallel arrangement, that is:

1st. Is just 1 resistance of 100.0 Ohm.

2nd.

$\frac{1}{R_{\text{total}}}=\frac{_{}1}{70.0\Omega}+\frac{1}{70.0\Omega}\Rightarrow\frac{1}{R_{\text{total}}}=\frac{2}{70.0\Omega}$$\Rightarrow R_{\text{total}}=\frac{70.0}{2}\Omega\Rightarrow R_{total}=35.0\Omega$

So, the two resistances in parallel are equivalent to 35.0 Ohm.

3rd.

$\frac{1}{R_{\text{total}}}=\frac{1}{40.0\Omega}+\frac{1}{40.0\Omega}+\frac{1}{40.0\Omega}\Rightarrow\frac{1}{R_{\text{total}}}=\frac{3}{40.0\Omega}$$\Rightarrow R_{\text{total}}=\frac{40.0}{3}\Omega\Rightarrow R_{\text{total}}\approx13.3\Omega$

So, the three resistances are equivalent to 40.0 / 3 Ohm.

Then we find the equivalent resistance of the resulting serial resistances:

$R_{\text{FINAL}}=100.0\Omega+35.0\Omega+\frac{40.0}{3}\Omega\Rightarrow R_{\text{FINAL}}=\frac{445}{3}\Omega$$\Rightarrow R_{\text{FINAL}}\approx148.3\Omega$

So, the equivalent resistance of the resistors in the circuit is 445/3 Ohms, that is approximately 148.3 Ohms.