Four resistors each of resistance 5 Ω are connected in parallel. What is the effective resistance?
Give,
R1 = R2 = R3 = R4 = 5 Ω
In parallel, if the equivalent resistance is RP, then
1RP=1R1+1R2+1R3+1R41RP=15+15+15+151RP=45⇒RP=54⇒RP=1.25Ω\dfrac{1}{R_P} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} + \dfrac{1}{R_4} \\[1em] \dfrac{1}{R_P} = \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5} \\[1em] \dfrac{1}{R_P} = \dfrac{4}{5} \\[1em] \Rightarrow R_P = \dfrac{5}{4} \\[1em] \Rightarrow R_P = 1.25 ΩRP1=R11+R21+R31+R41RP1=51+51+51+51RP1=54⇒RP=45⇒RP=1.25Ω
Hence, equivalent resistance = 1.25 Ω
