a, \(\xi_b=\xi_1+\xi_2=7,5+7,5=15\left(V\right)\)
\(r_b=r_1+r_2=1+1=2\left(\Omega\right)\)
b,\(R=\dfrac{R_2\cdot\left(R_1+R_3\right)}{R_2+R_1+R_3}=\dfrac{40\cdot\left(40+20\right)}{40+40+20}=24\left(\Omega\right)\)
\(I=\dfrac{\xi_b}{R+r_b}=\dfrac{15}{24+2}=\dfrac{15}{26}\left(A\right)\)
c,\(U_{AB}=I\cdot R=\dfrac{15}{26}\cdot24=\dfrac{180}{13}\left(V\right)\)
\(I_{AD}=I_{DB}=I_{AB}=\dfrac{U_{AB}}{R_1+R_3}=\dfrac{\dfrac{180}{13}}{40+20}=\dfrac{3}{13}\left(A\right)\)
\(U_{AD}=R_1I_{AD}=40\cdot\dfrac{3}{13}=\dfrac{120}{13}\left(V\right)\)
\(U_{DB}=R_1I_{DB}=20\cdot\dfrac{3}{13}=\dfrac{60}{13}\left(V\right)\)
d,\(P_1=U_{AD}\cdot I_{AD}=\dfrac{120}{13}\cdot\dfrac{3}{13}=\dfrac{360}{169}\left(W\right)\)
\(P_2=\dfrac{U_{AB}^2}{R_2}=\dfrac{\left(\dfrac{180}{13}\right)^2}{40}=\dfrac{810}{169}\left(W\right)\)
\(P_3=U_{DB}\cdot I_{DB}=\dfrac{60}{13}\cdot\dfrac{3}{13}=\dfrac{180}{169}\left(W\right)\)
e,\(A_1=P_1t=\dfrac{360}{169}\cdot300\approx639,05\left(J\right)\)
\(P_b=I^2R=\left(\dfrac{15}{26}\right)^2\cdot24=\dfrac{1350}{169}\left(W\right)\)