Question

Find the potential difference across each resistor in the figure below. (R₁ = 4.60 ?, R₂ = 4.20 ?, R₃ = 2.80 ?, R₄ = 1.80 ?)??

12.0 V 8.00 V 18.0 V

?V1 =
?V2 =
?V3 =
?V4 =

Answer 1

12.0 V 213.00 V18.0 V R.

$\sum I_{in}=\sum I_{out}$

--------------(i)

$\bigtriangleup V=I.R$

$-R_2I_3-R_1I_1+12-3=0$

$-4.20I_3-4.60I_1+9=0$

$\frac{-4.20I_3}{4.60}+\frac{9}{4.60}=\frac{4.60I_1}{4.60}$

$-0.913I_3+1.95=I_1$ ---------------(ii)

$-3-R_2(I_3)-R_3(I_2)-R_4(I_2)+18=0$

$15-4.20(I_3)-2.80(I_2)-1.80(I_2)=0$

$15-4.2I_3=4.6I_2$

$\frac{15}{4.6}-\frac{4.2I_3}{4.6}=\frac{4.6I_2}{4.6}$

$3.26-0.913I_3=I_2$  ----------------(iii)

substituting equations (ii) and (iii) in eq (i)

$(-0.913I_3+1.95)+(3.26-0.913I_3)=I_3$

$5.21=2.826I_3$

$I_3=1.8436A$

$I_2=1.5768A$

$I_1=0.2668A$

The potential difference is $\bigtriangleup V=I.R$ , then the potential difference across each resistor are

$\Delta V_1=I_1R_1=0.2668(4.60)=1.227 V$

$\Delta V_2=I_2R_3=1.5768(2.80)=4.415V$

$\Delta V_4=I_2R_4=1.5768(1.80)=2.838V$

$\Delta V_3=I_3R_2=1.8436(4.20)=7.743V$