3.You have a 15Omega and 25Omega resistor in paralle!What is the total resistance? 4. You have a 15Omega and 25Omega resistor in series What is the total resistance?

3. To find the total resistance of two resistors in parallel, we can use the formula:<br /><br />\[<br />\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2}<br />\]<br /><br />where \(R_{\text{total}}\) is the total resistance, and \(R_1\) and \(R_2\) are the resistances of the two resistors.<br /><br />Given that \(R_1 = 15\Omega\) and \(R_2 = 25\Omega\), we can substitute these values into the formula:<br /><br />\[<br />\frac{1}{R_{\text{total}}} = \frac{1}{15} + \frac{1}{25}<br />\]<br /><br />To add these fractions, we need a common denominator. The least common multiple of 15 and 25 is 75. So, we rewrite the fractions with a denominator of 75:<br /><br />\[<br />\frac{1}{R_{\text{total}}} = \frac{5}{75} + \frac{3}{75}<br />\]<br /><br />Now, we can add the fractions:<br /><br />\[<br />\frac{1}{R_{\text{total}}} = \frac{8}{75}<br />\]<br /><br />To find \(R_{\text{total}}\), we take the reciprocal of both sides:<br /><br />\[<br />R_{\text{total}} = \frac{75}{8} = 9.375\Omega<br />\]<br /><br />So, the total resistance of the two resistors in parallel is \(9.375\Omega\).<br /><br />4. To find the total resistance of two resistors in series, we simply add their resistances together:<br /><br />\[<br />R_{\text{total}} = R_1 + R_2<br />\]<br /><br />Given that \(R_1 = 15\Omega\) and \(R_2 = 25\Omega\), we can substitute these values into the formula:<br /><br />\[<br />R_{\text{total}} = 15 + 25 = 40\Omega<br />\]<br /><br />So, the total resistance of the two resistors in series is \(40\Omega\).