Two capacitors $$C$$ and $$\frac{C}{2}$$ are connected to a battery of $$V$$ volts, as shown below
The work done in charging both the capacitors fully is
A series R-C circuit is connected to AC voltage source. Consider two cases; (A) When C is without a dielectric medium and (B) When C is filled with dielectric of constant 4. The current I$$_R$$ through the resistor and voltage V$$_C$$ across the capacitor are compared in two cases.
A space ship is launched into a circular orbit close to earth’s surface. What additional velocity has now to be imparted to the spaceship in the orbit to overcome the gravitational pull?
(Radius of earth = 6400 km, g = 9.8 m/s$$^2$$)
A force $$\mathbf{F}=-k(y \hat{\mathbf{i}}+x \hat{\mathbf{j}})$$ where $$k$$ is a positive constant, acts on a particle moving in the $$x y$$ plane. Starting from the origin, the particle is taken along the positive $$x$$-axis to the point $$(a, 0)$$ and then parallel to the $$y$$-axis to the point $$(a, a)$$. The total work done by the force on the particle is