Physics – 4.3.2 Series and parallel circuits | e-Consult

Concept Used: The p.d. across an arrangement of parallel resistances is the same as the p.d. across one branch in the arrangement of the parallel resistances. The voltage across parallel resistors is the same. We can use Ohm's Law to calculate the current through each resistor and then find the p.d. across each.

Solution:

1. Calculate the total resistance: The equivalent resistance (R_eq) of two resistors in parallel is: 1/R_eq = 1/R₁ + 1/R₂ = 1/10Ω + 1/20Ω = 3/20Ω. Therefore, R_eq = 20/3Ω ≈ 6.67Ω.
2. Calculate the total current: The total current (I) flowing from the battery is: I = V/R_eq = 12V / (20/3Ω) = 12V * (3/20Ω) = 1.8A.
3. Calculate the p.d. across R₁: The p.d. (V₁) across R₁ is: V₁ = I * R₁ = 1.8A * 10Ω = 18V.
4. Calculate the p.d. across R₂: The p.d. (V₂) across R₂ is: V₂ = I * R₂ = 1.8A * 20Ω = 36V.

Answer: The p.d. across R₁ is 18V and the p.d. across R₂ is 36V.