TextBook Solutions
- A parallel plate capacitor with air between the plates has a capacitance of 8 pF (lpF = 10-12F). C = 8pF, C = fracε₀ ~A~d C' = fracε_r ε₀ ~Ad/2 = 2ε_r ∴ C' = 2 x 6 x 8 x 10⁻¹² F = 96 pF 1
- In a parallel plate capacitor with air between the plates, each plate has an area of 6 x 10-3 m2 A = 6 x 10⁻³ m² d = 3 mm = 3 x 10⁻³m C = fracε₀ ~A~d = frac8.85 × 10⁻¹² × 6 × 10⁻³3 × 10⁻³ = 17.70 x 10⁻¹² = 17.7 pF Q = CV = 17.7 x 10⁻¹² x... 1
- A 12pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor? C = 12 pF, V = 50V E = 1 / 2 CV² = 1 / 2 x 10⁻¹² x 50 x 50 = 150 x 10⁻¹⁰ = 1.5 x 10⁻⁸ J 1
- Show that the force on each plate of a parallel plate capacitor has a magnitude equal to \(\frac { 1 }{ 2 }\) QE, where Force = 1 / 2 QE Work done = 1 / 2 V x Q The physical origin of the factor 1 / 2 in the force formula lies in the fact that just outside the... 2
- A μ piF capacitor is charged by a 200 V supply. It is then disconnected from the supply C₁ = 4 x 10⁻⁶F V = 200 V C₂ = 2 x 1o⁻⁶F E₁ = 1 / 2 C₁V² = 1 / 2 x 4 x 10⁻⁶ x 200 x 200 = 8 x 1o⁻² Q = C₁V = 4 x 10⁻⁶ x 200 = 8 x 10⁻⁴ C E₂ =... 1
- (a) Are potential difference and potential energy the same? (b) If they are not the same, then define them. (a) No. The potential difference is a field property. Potential energy is the interaction energy of charge configuration. (b) The electrosta... 1
- A proton and an electron move between two points having a potential difference V. (a) Both gain the same energy Work done = energy gain = Potential difference x Charge The p.d and charge are the same for each. (b) One eV i... 1
- ‘Work is done on the charge ’. What do you understand by this? While moving the charge, work is to be done against repulsion of the field. 1
- What is the potential difference between the surface and interior point of the charged conductor? The potential at every point in a charged conductor is the same and is equal to the potential on the surface. Therefore the potential differ... 1
- How can we increase the capacitance of a conductor? By increasing the linear dimension. 2
- How will the applied voltage be divided among the capacitors? In a series combination, the applied voltage divides among the capacitors in inverse proportion to their capacitances: V ∝ 1/C . In series,... 1
- In which form and where is the energy of the capacitor stored? Electrical energy and is stored between the plates in the form of the electric field. 1
- Classify the following molecules into (a) Polar and non-polar. (H2O, H2, NH3, N2, CO2, CO, HCl, O2) (a) Polar molecules: H2O, NH3, CO, HCl Non-polar molecules: H2, N2, CO2, and O2 (b) polar and non-polar molecules: A molecule is said to be... 1
- Two copper spheres of radii, one hollow and the other solid are charged to the same potential. Both will hold the same charge No The capacity is small 2
- How much work is done in moving a 500 pC charge between two points on an equipotential surface? zero the work done in moving the given charge between two equipotential surfaces is equal to zero. 1
- What are the key features of a list in Python Class 12? Answer: A Python list is an ordered, mutable sequence that can hold items of any type, written inside square brackets. Key features of a lis... 1
- If A and B are two events such that A ⊂ B and P(B) ≠ 0, then which of the following is true? A ⊂ B ⇒ A ∩ B = A ⇒ P(A ∩ B) = P(A) ∴ P(A/B) = P(A∩B)/P(B) = P(A)/P(B) But P(B) ≤ 1 ⇒ P(A/B) ≥ P(A). 1
- A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. Box contains 12 good and 3 bad oranges. If three oranges selected are good ones, the box is approved for sale. 3 good oranges may be selecte... 1
- A fair coin and an unbiased dice are tossed. Let A be the event ‘head appears on the coin’ and B be the event 3 on dice When a coin is thrown, head or tail will occur. ∴ Probability of getting head P(A) = 1/2 . when a dice is tossed 1, 2, 3, 4, 5, 6 one of the... 1
- A dice, marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event ‘number is even’ Even numbers on dice are 2, 4, 6. ∴ Probability of getting an even number = P(A) = 3/6 = 1/2 . There are two colours on the dice viz. red an... 1
- A dice is tossed thrice. Find the probability of getting an odd number at least once? If a dice is thrown and an odd number occurs, then it may result in 1, 3, 5. ∴ The probability of getting an odd number in a throw of a dice... 1
- Problem of solving specific problem independently by A and B are \(\frac{1}{2}\) and \(\frac{1}{3}\) respectively. Probability that A solves the problem = 1/2 ⇒ Probability that A does not solve the problem P( A ) = 1 – 1/2 = 1/2 . Probability that B solv... 1
- In a hostel, 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi (a) Let A be the event that a student reads Hindi newspaper, and B be the event that a student reads English newspaper. We are asked to find... 1
- The probability of obtaining an even prime number on each die, when a pair of dice is rolled is There are only one even prime number, i.e., 2, when a dice is rolled, the probability of getting an even prime number = 1/6 . When two dice... 1