Fysik opgaver EL (Rep)

Opgave 1

A: $LaTex: R = \left(\frac{1}{5\Omega}+\frac{1}{81\Omega}\right)^{-1} + 200\Omega = 204,79\Omega\\$

B: $LaTex: R = \left(\frac{1}{120\Omega}+\frac{1}{5\Omega+21\Omega}\right)^{-1} = 21,37\Omega\\$

C: $LaTex: R = \left(\frac{1}{4\Omega+14\Omega}+\frac{1}{70\Omega + \left(\frac{1}{\left(\frac{1}{3\Omega}+\frac{1}{2\Omega}\right)^{-1}}+\frac{1}{6\Omega+7\Omega} \right)^{-1}} \right)^{-1} = 14,364\Omega\\$

D: $LaTex: R = \left(\frac{1}{12\Omega + 33\Omega} + \frac{1}{50 \Omega} +\frac{1}{200\Omega}\right)^{-1} = 21,18\Omega$

E: $LaTex: R = \left(\frac{1}{2\Omega}+\frac{1}{6\Omega}\right)^{-1} + \left(\frac{1}{4\Omega}+\frac{1}{8\Omega}\right)^{-1} = 4,17\Omega$

A: $LaTex: \begin{eqnarray} U &=& 9V\\ I_2 &=& 0,2 A\\ R_2 &=& 22\Omega\\ U_2 &=& I_2\cdot R_2 = 4,4 V\\ \end{eqnarray}$

C: $LaTex: \begin{eqnarray} R_1 &=& 10 \Omega\\ I &=& \frac{U_1}{R_1} = 0,46A\\ \end{eqnarray}$

D: $LaTex: \begin{eqnarray} I_3 &=& I - I_2 = 0,26 A\\ R_3 &=& \frac{U_2}{I_3} = 16,92\\ \end{eqnarray}$

A: $LaTex: \begin{eqnarray} P &=& 3500 W\\ V_{vand} &=& 200l\\ \rho_{vand} &=& 1 \frac{kg}{l}\\ m_{vand} &=& \rho_{vand} \cdot V_{vand}\\ m_{jern} &=& 50kg\\ T_0 &=& 283,15 K\\ T_1 &=& 338,15 K\\ \Delta_T &=& T_1 - T_0\\ c_{jern} &=& 452 \frac{J}{kg\cdot K}\\ c_{vand} &=& 4182 \frac{J}{kg\cdot K}\\ C_{system} &=& c_{jern}\cdot m_{jern} + m_{vand} \cdot c_{vand} = 859 \frac{kJ}{K}\\ Q &=& \Delta_T \cdot C_{system} = 47245 kJ\\ t &=&\frac{Q}{P} = 13,5 ks = 3,75 t\\ \end{eqnarray}$

B: $LaTex: \begin{eqnarray} U &=& 220 V\\ I &=& \frac{P}{U} = 15,91 A\\ \end{eqnarray}$

C: $LaTex: \begin{eqnarray} R &=& \frac{U}{I} = 13,83\Omega\\ \end{eqnarray}$

D: $LaTex: \begin{eqnarray} d &=& 0,8 cm = 0,008 m\\ l &=& 60 cm = 0,6 m\\ A &=& \left(\frac{d}{2}\right)^2\cdot\pi\\ \rho &=& \frac{R\cdot A}{l} = 1,16 \cdot 10^{-3} \Omega\cdot m\\ \end{eqnarray}$