Electronic – Can Resistance of wires be ignored

Have you covered equivalent resistances? Essentially, it is a way to combine resistors in series or parallel until you get a single resistance, working your way from out to in.

Let's say you want to find \$R_{AB}\$.

First, your have a series combination \$R_5\$, \$R_6\$, and \$R_7\$. $$ R_{5,6,7} = R_5 + R_6 + R_7 = 18 \Omega $$

^{simulate this circuit – Schematic created using CircuitLab}

Now you have a parallel combination between \$R_4\$ and \$R_{5,6,7}\$. $$ R_{4,5,6,7} = \frac{R_4 \cdot R_{5,6,7}}{R_4 + R_{5,6,7}} = 3.27 \Omega $$

^{simulate this circuit}

You are almost done! Now, since you are looking for the equivalent resistance between A and B, you have a series combination for \$R_2\$, \$R_3\$ and \$R_{4,5,6,7}\$: $$ R_{2,3,4,5,6,7} = R_2 + R_3 + R_{4,5,6,7} = 8.27 \Omega $$

^{simulate this circuit}

Last Step!

You have a parallel combination between \$R_1\$ and \$R_{2,3,4,5,6,7}\$: $$ R_{AB} = \frac{R_1 \cdot R_{2,3,4,5,6,7}}{R_1 + R_{2,3,4,5,6,7}} = 0.892\Omega $$

Think everything you have on the circuit a resistor even the wires to connect different component. In ideal condition the resistance of a wire is 0 Ohm. We make short circuits with wires. Therefore the resistance of the short circuit is 0 Ohm. Now if you calculate equivalent resistance of the 20 Ohm and 0 Ohm resistor then you get 0 Ohm.

The theory here is, the resistor of 0 Ohm has a conductance of infinity (1/0= infinity). When there is two resistor in parallel then the current divides itself accordance to conductance of the resistors. The more conductance the more current. Here we have a resistor with unlimited conductance, so all current flows through it. Therefore, the other resistor has no effective value. That’s why the 20 Ohm resistor can be ignored.

In practical circuits, the short circuit resistance is not zero but small enough to consider it zero for practical use.