Answer to Question #179953 in Electric Circuits for William McNutt

Question

1. A parallel circuit contains four 1.5 volt batteries and three resistances of 5.0, 2.5 and 4.0 - What is the total emf?
2. What is the total resistance of this circuit?
3. What current does the parallel circuit above draw?

Thank you

Answer 1

(1)

$E_{res}=\dfrac{\dfrac{E_1}{R_1}+\dfrac{E_2}{R_2}+\dfrac{E_3}{R_3}}{\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}}$

$E_{res}=\dfrac{1.5(\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3})}{(\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3})}=1.5\space V$

(2) $\dfrac{1}{R_{res}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}$

$\Rightarrow \dfrac{1}{R_{res}}=\dfrac{1}{5}+\dfrac{1}{2.5}+\dfrac{1}{4}$

$\Rightarrow R_{res}=\dfrac{20}{17}=1.17\space\Omega$

(3) $I_{res}=\dfrac{E_{res}}{R_{res}}=\dfrac{1.5}{1.17}$

$\Rightarrow I_{res}=1.282\space A$