Resistors of 10 Ω and 30 Ω are connected in parallel across 20 V. Find equivalent resistance and total current.

Solution & explanation

1. Given: R₁ = 10 Ω; R₂ = 30 Ω; V = 20 V.

2. Add reciprocals for parallel resistors.

   $$\frac{1}{R}=\frac{1}{30}+\frac{1}{10}$$

3. Use common denominator 30.

   $$\frac{1}{R}=\frac{1}{30}+\frac{3}{30}=\frac{4}{30}$$

4. Take reciprocal.

   $$R=\frac{30}{4}=7.5$$

5. Each branch has the full 20 V. Apply I = V/R to each.

   $$I_1=\frac{20}{10}=2$$

6. Find the second branch current.

   $$I_2=\frac{20}{30}=\frac{2}{3}$$

7. Add branch currents.

   $$I=\frac{2}{3}+2=\frac{8}{3}$$

8. State the result with units: R = 7.5 Ω; total I ≈ 2.67 A.

R = 7.5 Ω; I ≈ 2.67 A