LETTER C
Using the graph, we will write two functions using the equation of electrical generators:
\(U=\varepsilon-r\cdot i\)
{ 20=ε-5∙r 14=ε-8∙r
Next, we will solve the system by multiplying the second equation by -1 and adding the equations:
{ 20=ε-5∙r -14=-ε+8∙r
\(20-14=-5\cdot r+8\cdot r\)
\(6=3\cdot r\)
\(r=\frac{6}{3}\)
\(r=2\ \Omega\)
Now, we substitute the resistance value in the first equation and obtain the emf:
\(20=\varepsilon-5\cdot r\)
\(20=\varepsilon-5\cdot2\)
\(20=\varepsilon-10\)
\(\varepsilon=20+10\)
\(\varepsilon=30\ V\)
Finally, we will find the value of the short-circuit current that occurs when the electrical voltage is zero. To do this, we will again use the equation for electrical generators:
\(U=\varepsilon-r\cdot i\)
\(0=30-2\cdot i\)
\(-30=-2\cdot i\)
\(30=2\cdot i\)
\(i=\frac{30}{2}\)
\(i=15\ A\)