Three Resistors are connected across a 24V battery in parallel. Find (a) Equivalent Resistance

Question

Three Resistors are connected across a 24V battery in parallel.

R1= 4Ω R2 = 8Ω R3 = 12Ω

Find (a) Equivalent Resistance of the Circuit

(b) Current in each Resistor

Answer 1

first, find the currents. In each resistor branch the current is simply E/R

Having found the 3 currents, simply add them up for a total of 11 amps

The equivalent resistance is then: R = E/I = 24/11 = 2.182 ohms

Answer 2

Since the resistors are connected in parallels

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃

OR 1/R_eq = 1/4 + 1/8 + 1/12

1/R_eq = 176/384 ∴ R_eq = 384 /176 = 2.18 Ω

(Part a) R_eq = 2.18 Ω

(b) Find Current in each Resistor

I₁ = ΔV/R₁ = 24V / 4Ω = 6.0 Amp

I₂ = ΔV/R₂ = 24V / 8Ω = 3.0 Amp

I₃ = ΔV/R₃ = 24V / 12Ω = 2.0 Amp