Question

Three 15.0-W resistors are connected in parallel across a 30.0-V battery. Please show all work.

a) Find the current through each branch of the circuit.
b) Find the equivalent resistance of the circuit.
c) Find the current through the battery.

Answer 1

Part A)

Since all of the resistors have equal resistance, hence for finding even only 1 branch It will be fine because current will be the same for all branches.

=>
`I = (V)/(R_(1) )`

=>
`I = (30)/(15)`

=> I = 2 A

Part B)

Equivalent resistance for parallel circuits is the sum of reciprocals of each resistor.

=>
`(1)/(R) = (1)/(R_(1))+(1)/(R_(2)) +(1)/(R_(3))`

=>
`(1)/(R) = (1)/(15)+ (1)/(15)+(1)/(15)`

=>
`(1)/(R) = (3)/(15)`

=> R = 15/3

=> R = 5 ohms

Part C)

I = V/R

Where I is current, V is voltage and R is the equivalent resistance

=> I = 30/5

=> I = 6 A