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# if Voltage source is 12, resistance is 6800 and voltage 1 is 8 what is R2

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if Voltage source is 12, resistance is 6800 and voltage 1 is 8 what is R2

physics
Jan 8, 2015

#1
+24342
+5

if Voltage source is 12, resistance is 6800 and voltage 1 is 8 what is R2

$$\small{\text{series circuit }}\\ \small{\text{ R=6800\ \Omega \quad U = 12\ V\quad U_1 = 8\ V\quad R_2=\ ? \ \Omega  }}\\ \small{\text{ I.  \quad I=\frac{R_1}{U_1}=\frac{R_2}{U_2} \quad \Rightarrow \quad \boxed{R_2=\frac{U_2}{U_1}*R_1}  }}\\\\ \small{\text{ II.  \quad R=R_1+R_2 \quad \Rightarrow \quad \boxed{R_1=R-R_2}  }}\\\\ \small{\text{ III.  \quad U=U_1+U_2 \quad \Rightarrow \quad \boxed{U_2=U-U_1}  }}\\\\ \small{\text{ we substitute U_2=U-U_1  and R_1=R-R_2 }}\\\\ \small{\text{  R_2=\left(\frac{U-U_1}{U_1}\right) *(R-R_2)\quad \Rightarrow \quad \boxed{{ R_2 = \left( 1-\frac{U_1}{U} \right) *R } }  }} \\\\ \small{\text{  R_2 = \left( 1-\frac{8\ V}{12\ V} \right) * 6800 \ \Omega = \left( 1-\frac{2}{3} \right) * 6800 \ \Omega =\frac{1}{3}* 6800 \ \Omega =2266.\overline{6} \ \Omega  }} \\\\ \small{\text{  {R_2 = 2266.\overline{6} \ \Omega }  }}$$

.
Jan 9, 2015

#1
+24342
+5

if Voltage source is 12, resistance is 6800 and voltage 1 is 8 what is R2

$$\small{\text{series circuit }}\\ \small{\text{ R=6800\ \Omega \quad U = 12\ V\quad U_1 = 8\ V\quad R_2=\ ? \ \Omega  }}\\ \small{\text{ I.  \quad I=\frac{R_1}{U_1}=\frac{R_2}{U_2} \quad \Rightarrow \quad \boxed{R_2=\frac{U_2}{U_1}*R_1}  }}\\\\ \small{\text{ II.  \quad R=R_1+R_2 \quad \Rightarrow \quad \boxed{R_1=R-R_2}  }}\\\\ \small{\text{ III.  \quad U=U_1+U_2 \quad \Rightarrow \quad \boxed{U_2=U-U_1}  }}\\\\ \small{\text{ we substitute U_2=U-U_1  and R_1=R-R_2 }}\\\\ \small{\text{  R_2=\left(\frac{U-U_1}{U_1}\right) *(R-R_2)\quad \Rightarrow \quad \boxed{{ R_2 = \left( 1-\frac{U_1}{U} \right) *R } }  }} \\\\ \small{\text{  R_2 = \left( 1-\frac{8\ V}{12\ V} \right) * 6800 \ \Omega = \left( 1-\frac{2}{3} \right) * 6800 \ \Omega =\frac{1}{3}* 6800 \ \Omega =2266.\overline{6} \ \Omega  }} \\\\ \small{\text{  {R_2 = 2266.\overline{6} \ \Omega }  }}$$

heureka Jan 9, 2015
#2
+108608
0

Thank you Heureka

I am going to reference this from the LaTex page too.  Thanks again :)

Jan 9, 2015