Question

Please include diagrams:

a) A 100-W light bulb and a 40-W light bulb are both rated at household voltage. i) Which light bulb will be brighter if the two bulbs are connected in parallel and this combination connected to a household voltage source? ii) Which light bulb will be brighter if they are connected in series and this combination connected to a household voltage? b) A battery charges a parallel plate capacitor. After it is fully charged, it is then disconnected from the battery and the gap between the plates is filled with a dielectric. How does the charge on the plates and the potential difference between them change? c) A battery is used to charge a parallel plate capacitor. After it is fully charged, the battery is disconnected and the plates are pulled apart. What happens to the potential energy stored in the capacitor and the potential difference across the capacitor?

Answer 1

(a)

(i) when bulbs are connected in parallel then the voltage across them must be same.
We know that power is given by
P = V² /R , therefore
R = V²/P
Since voltage is same in parallel therfore the bulb with 100 W power will have less resistance
hence 100 W bulb will be more brighter.
(ii) When they are connected in series then the current through them will be same.
We know that
P = I²R , therfore
R = P/I²
hence the 100 W bulb will have more resistance therfore 40 W bulb will be more brighter.
(b) On disconnecting the battery the charge on the capacitor will remain same.
When we insert dielectric material then it will increase the capacitance as
C' = kC_o
where k is dielectric constant.
We know that
V = Q/C
Since the capacitance has increased therefore the potential difference(V) will decrease.
(d) When the plates will be pulled away then the capacitance will decrease because
C = e_oA/d , so on increasing d capacitance will decrease, therefore
potential difference will inrease.
We know that potential energy is given by = (1/2)QV
since charge is constant and voltage (potential difference) has increased therfore the potential energy will also increase.