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}+(1)/(70.0\Omega)\Rightarrow\frac{1}{R_{\text{total}}}=(2)/(70.0\Omega)`
`\Rightarrow R_{\text{total}}=(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}}}=(1)/(40.0\Omega)+(1)/(40.0\Omega)+(1)/(40.0\Omega)\Rightarrow\frac{1}{R_{\text{total}}}=(3)/(40.0\Omega)`
`\Rightarrow R_{\text{total}}=(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+(40.0)/(3)\Omega\Rightarrow R_{\text{FINAL}}=(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.