Calculate the effective resistance of a 5 Ω resistor and a 7 Ω resistor when they are connected in parallel. - Leaving Cert Physics - Question (i) - 2018

Substituting the resistor values into the formula gives:

$\frac{1}{R_T} = \frac{1}{5} + \frac{1}{7}$

First, find a common denominator to add the fractions. The common denominator for 5 and 7 is 35:

$\frac{1}{R_T} = \frac{7}{35} + \frac{5}{35} = \frac{12}{35}$

Now, taking the reciprocal to find $R_T$:

$R_T = \frac{35}{12} \approx 2.92 \Omega$

Thus, the effective resistance is approximately $2.9 \Omega$.