2014 H2 P2 solutions vjc

1 Nov 2014 H2 P2 solutions: 1(a)(i) If force X is zero, then force Y alone must balance the weight. Hence, magnitude of Y = 60.0 N, and direction of Y is upwards. So,  = 90o. (ii) For equilibrium, net horizontal force = 0 ∴ߠݏ݋ܻܿ= ݏ݋ܿܺ30௢ ∴ܻ௛ = 200ݏ݋ܿ30௢ = 173ܰ Also, net vertical force = 0 ∴ܻ௩ +݊݅ݏܺ30௢ −ܹ= 0 ܻ௩ + 200݊݅ݏ30௢ − 60.0 = 0 ∴ܻ௬ = −40.0ܰ ∴ܻ= ටܻ௫ ଶ +ܻ௬ ଶ = ඥ173ଶ + (−40)ଶ = ૚ૠૡ ۼ ߠ݊ܽݐ= ܻ௬ ܻ௫ = −40.0 173 ∴ߠ= −૚૜. ૙࢕ or 347o. 1(b) Force X has a non-zero horizontal component to the right, which must be balanced by non-zero horizontal component of force Y which can only exist if rope B is inclined to the left and not exactly vertical in direction.

2 2(a) p-type doping introduces Group 3 atoms such as indium or boron into the semiconductor material. This introduces new energy levels called acceptor levels, which are just above the valence band of the silicon atoms. Electrons at the top of the valence band of silicon are able to jump up into these acceptor levels, leaving behind holes in the valence band allowing valence band electrons to gain energy from an externally applied electric field and jump into them, implying that the electrons are able to move within the silicon solid. Thus, the electrical conductivity is increased. (b) In a p-n junction, an electrical p.d. exists across the depletion region with the n-side at a higher potential, and this p.d. prevents any net migration of electrons and holes across the junction. When an external p.d. is applied across the p-n junction in the forward-biased direction (see Fig. 1), this p.d. across the junction is reduced (depletion region narrows), making it easier for charges to diffuse across the junction, resulting in a net current flow in the p to n direction. When an external p.d. is applied across the p-n junction in the reverse-biased direction (see Fig. 2), this p.d. across the junction is increased (depletion region widens), making it harder for charges to diffuse across the junction, so that the current is effectively reduced to zero. In this way, the p-n junction can serve as a rectifier. P-type semiconductor N-type semiconductor + Fig. 1: Forward bias P-type semiconductor N-type semiconductor + Fig. 2: Reverse bias

3 3(a) As the resistance of R is increased from 0 to 12 , the terminal p.d. will increase. This is because, with a larger value of R, the external circuit resistance accounts for a larger fraction of the total circuit resistance, and so the p.d. across the external resistance will increase according to the potential-divider rule. (b)(i) By the potential-divider rule, Terminal p.d. = ସ.଴ାଷ.ହ ସ.଴ାଷ.ହା଴.ଶହ × 5.0 = 4.84 V. (ii) Efficiency of power transfer is given by: efficiency = power dissipated in external load total power dissipated =ܲ௘௫௧௘௥௡௔௟ ܲ௧௢௧௔௟ =ܫܸ ܫܧ where V = terminal p.d., and E = e.m.f. of cell. ⇒ efficiency = ܸ ܧ= 4.84 5.0 = 0.968 ≈ ૢૠ % (c) (i) p.d. across PJ = 1.2 V. [Explanation: