Home/ Questions/Find the current in the 3.00 resistor. (Note that three currents are given.)
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Asked: 2022-04-13T03:54:17+00:00 In:

Find the current in the 3.00 resistor. (Note that three currents are given.)

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26.23)%201.Find%20the%20current%20in%20the%203.00%20resistor.%20(Note%20that%20three%20currents%20are%20given.)%202.Find%20the...

1.Find the current in the 3.00 Ω resistor. (Note that three currents are given.)

2.Find the unknown emfs ε1 and ε2.

3.Find the resistance R .

♦ Relevant knowledge
The electromotive force (also known as emf) is the term used to describe the amount of energy per unit of charge transferred from an energy source. The electromotive force may also be called voltage or potential difference within the circuit. The frequency describes the properties of EMF.

 

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2 Answers

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    Expert

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  2. Concepts and Reason

    Kirchhoff’s junction rule and Ohm’s law are the concepts that will solve this problem.

    First, from the given currents, find the current in the3.00Q resistor. Find the unknown emfs using Kirchhoff’s voltage law. Similar to the Kirchhoff voltage law, you can find the unknown resistance.

    Fundamentals

    Ohm’s law says that the current between two points of a circuit is proportional the potential difference between them. The resistance is the constant of proportionality.


    V IR

    is the potential difference. is current, and #media_tag_4$ is resistance.

    Kirchhoff’s circuit laws that govern current and voltage are used in electrical circuits. Kirchhoff’s current law says that the total amount of current entering a node is equal to its total output.

    Kirchhoff’s voltage law says that the total voltage around closed loops is zero.


    (26.23.1)

    Below is a diagram showing the current direction through the circuit.



    R 2.00A ి E1 h f b 4.00 3.002 6.00S 3.00AV 5.00A с e d కా

    The current in the linebc and in the linefe combine and flow together through the linehd as current.

    The current line hd is given by


    be fe

    Here, be is the current in the linebc andis the current in the linefe .

    Substitute3.00 A forbe and5.00 A forto find the current.


    I = 3.00 A +5.00 A =8.00 A


    (26.23.2.1)

    Kirchhoff’s voltage law is applied to loop bcdhb .

    |(3.00 A) (4.00)1 (3.002)= e

    Substitute8.00A forto find the emf.


    (3.00 A) (4.00)+(8.00 A) (3.002)= c,

    The emf is


    & 12V+24V =36V


    (26.23.2.2)

    Kirchhoff’s voltage law is applied to loop hdefh .

    |(5.00 A) (6.00s2)+1 (3.00 2)=E,

    Substituteforto find the emf&2 .


    (5.00 A) (6.00)+(8.00 A)(3.00) c, =

    The emf &2 is


    30V 24V E =54V


    (26.23.3)

    Kirchhoff’s voltage law is applied to loop abfga .

    &2-6( (2A)R R=-& 2A

    Substitute36 V forand 54 V for&2 to find the resistanceR .


    54V -36 V R = 2A 18V 2A =90

    Ans: Part 26.3.1

    The current in the 3.00Q is8.00 A

    Part 26.23.2.1

    The emfis36V

    Part 26.23.2.2

    The emf&2 is54 V

    Part 26.23.3

    The resistanceR is.

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