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6 January, 13:07

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?

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  1. 6 January, 13:51
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    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

    I = 0.83A
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