Parallel Circuit Physics Example 1

Solution

1. 1
   Total resistance: $$\frac{1}{R_T} = \frac{1}{6} + \frac{1}{12} = \frac{2}{12} + \frac{1}{12} = \frac{3}{12} \implies R_T = 4 \text{ } \Omega$$
2. 2
   Current through $6 \text{ } \Omega$: $I_1 = \frac{V}{R_1} = \frac{12}{6} = 2 \text{ A}$.
3. 3
   Current through $12 \text{ } \Omega$: $I_2 = \frac{V}{R_2} = \frac{12}{12} = 1 \text{ A}$.
4. 4
   Total current: $I_T = 2 + 1 = 3 \text{ A}$ (consistent with $V/R_T = 12/4 = 3 \text{ A}$).