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Dao asked in Science & MathematicsPhysics · 2 months ago

The resistance R = 10.0 Ohms and ε1 = 13.3 V and ε2 = 18.7 V. What is the current through the Resistor R at the bottom of the circuit ?

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  • 2 months ago

    Let the left side be Node Vx and the right side = ground. Now write an equation for the currents leaving Vx = 0 by KCL

    (Vx-13.3)/10 + (Vx-18.7)/10 + Vx/10 = 0

    Multiply eq by 10

    3Vx = 13.3+18.7 = 32

    Vx = 32/3

    (32/3-13.3)/10 = -79/300 

    (32/3-18.7)/10 = -241/300

    32/3/10 = 320/300 = 16/15 A <<<<<

  • Knr
    Lv 4
    2 months ago

    for the circuit effective emf = 18.7 - 13.3 = 5.4 volt and effective resistance R’ = R/3 = 10/3 ohm

    and so total current is I = 5.4 / (10/3) = 1.62 amp.

    then, current through each resistor is i = 1.62 / 3 = 0.54 amp.

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  • 2 months ago

    Let the current from E2 is i2 & E1 is i1 & the current passing through the bottom resistance is i3,  BY the kirchoff's Laws:

    =>i1 + i2 = i3 ------------(i)

    By the upper loop:

    =>i1R - i2R = E1 - E2

    =>13.3 - 18.7 = 10(i1 - i2)

    =>i1 - i2 = -0.54 -----------------(ii)

    By the lower loop:

    =>18.7 = i2R + i3R 

    =>18.7 = 10(i2 + i1 + i2)  {as i3 = i1 + i2 -----------(i)}

    =>i1 + 2i2 = 1.87 ---------------(iii)

    By 2 x (ii) + (iii):

    =>3i1 = -2 x 0.54 + 1.87

    =>i1 = 0.26 amp

    By (ii:

    =>i2 = 0.54 + 0.26

    =>i2 = 0.80 amp

    Thus by (i):

    =>i3 = 0.26 + 0.80 = 1.06 amp

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  • oubaas
    Lv 7
    2 months ago

    E2 conducting

    Re2 = R+R/2 = 1.5 R

    I2' = 18.7/15 = 1.247 A 

    I1' = I3' = 1.247/2 A 

    E1 conducting 

    Re1 = R+R/2 = 1.5 R

    I1'' = 13.3/15 = 0.887 A

    I2'' = I3'' = 0.887/2 A 

    I3 = I3'+I3'' = 1.066 A 

    I1 = I1''-I1' = 0.887-1.247/2 = 0.263

    I2 = I2'-I2'' = 1.247-0.887/2 = 0.803

    V3 = I3*10 = 10.66 V 

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