A 5.0-Ω resistor and a 9.0-Ω resistor are connected in parallel. A 4.0-Ω resistor is then connected in series with this parallel combination. An ideal 6.0-V battery is then connected across the series-parallel combination of the three resistors.(a) What is the current through the 4.0-Ω resistor?
The 4ohm resistor is not parallel to any devices, so the current through it is the same as the total current through the circuit.
Apply I = V/R I = total current, V = battery voltage, R = total resistance
Calculate the total resistance R of the circuit first.
R will be the sum of the 4ohm resistor and the resistance of the 5&9ohm parallel resistors. To find the resistance of the pair, you apply the “sum of inverses” rule:
R = 1/(1/5 + 1/9) = 3.21ohm
Now add the 4ohm resistor: R = 3.21 + 4 = 7.21ohm
Now let’s calculate I = V/R: Given values: V = 6.0V R = 7.21ohm Plug in and solve for I: I = 6.0/7.21
