circuit analysisresistance
I'm so confused on how to find the equivalent resistance of this circuit. Initially, I calculated it to be R_eq = (1/(42+21)+1/63+1/(84+105))^-1 = 27 Ohms, but I think that's wrong.
I think that the 84 Ohm and 105 Ohm resistors are in series, but I don't know about the others.
There are two steps to finding the Thevenin equivalent circuit: finding the Thevenin voltage and the Thevenin resistance.
Thevenin voltage is the voltage across the two points you interested in (Vin). In this case it is easy to calculate as there is no current flowing in the 43 and 60 \$\Omega\$ resistors thus no voltage drop. Thus the voltage at Vin is the same as the voltage form the source, 72 V.
Thevenin resistance is calculated by 'turning off' all independent current and independent voltage sources and calculating the resistance between the two points. Turning off a voltage source sets the voltage across it to 0, which results in a short (0 \$\Omega\$) in parallel with the 275 \$\Omega\$ resistor. Any resistor combined in parallel with a short results in a short, leaving you with the 43 and 60 \$\Omega\$ resistors now in series, giving a Thevenin resistance of 103 ohms.
Putting the two together gives you a voltage source of 72 V in series with a 103 \$\Omega\$ resistor for you Thevenin equivalent circuit.
You're right. The three resistors 3 \$\Omega\$, are shorted, so that the equivalent resistance is the sum 3 + 3 = 6.
Best Answer
This is correct. They are in series, and you can combine them as such.
Once you have combined them, they will be in parallel with the 63Ω resistor, and you can combine again. Keep doing so, and you will find that the circuit reduces to a single equivalent resistor.