Answer to Question #196815 in Electric Circuits for gary

Question

A 35 ohms 55 ohms, and 85 ohm resistor are connected in parallel. The resistors are then connected to a 35-V battery. a) What is the equivalent resistance of the parallel circuit ?b. What is the current through each resistor? 

Answer 1

Given, $R_1=35,R_2=55,R_3=85$

(a) Equivalent resistance-

$\dfrac{1}{R_{eqv}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}\\[9pt]\dfrac{1}{R_{eqv}}=\dfrac{1}{35}+\dfrac{1}{55}+\dfrac{1}{85}\\[9pt]\dfrac{1}{R_{eqv}}=\dfrac{187+119+77}{6545}$

Taking Reciprocal-

$R_{eqv}=\dfrac{6545}{383}=17.08\Omega$

(b) As in parallel combination Voltage remains same

Current through each resistor is-

$i_1=\dfrac{V}{R_{1}}=\dfrac{35}{35}=1A\\[9pt]i_2=\dfrac{V}{R_{2}}=\dfrac{35}{55}=0.636A\\[9pt]i_3=\dfrac{V}{R_{3}}=\dfrac{35}{85}=0.41A$