A piece of wire with a resistance of 80Omega was cut into four equal parts . These parts were connected in parallel . Calculate the total resistance of circuit. 4Omega 20Omega 5Omega 0.2Omega

To solve this problem, we need to calculate the total resistance of the circuit when the four equal parts of the wire are connected in parallel.<br /><br />Given information:<br />- The original resistance of the wire is $80\Omega$.<br />- The wire is cut into four equal parts.<br />- The four parts are connected in parallel.<br /><br />Step 1: Calculate the resistance of each part.<br />Since the wire is cut into four equal parts, the resistance of each part will be:<br />Resistance of each part = Total resistance / Number of parts<br />Resistance of each part = $80\Omega / 4 = 20\Omega$<br /><br />Step 2: Calculate the total resistance of the parallel circuit.<br />When the four parts are connected in parallel, the total resistance can be calculated using the formula:<br />$1/R_{total} = 1/R_1 + 1/R_2 + 1/R_3 + 1/R_4$<br />where $R_1$, $R_2$, $R_3$, and $R_4$ are the resistances of the four parts.<br /><br />Substituting the values, we get:<br />$1/R_{total} = 1/20 + 1/20 + 1/20 + 1/20$<br />$1/R_{total} = 4/20$<br />$R_{total} = 20\Omega$<br /><br />Therefore, the total resistance of the circuit when the four equal parts of the wire are connected in parallel is $20\Omega$.<br /><br />The correct answer is $20\Omega$.