State Kirchhoff's second law.
- (a)State Kirchhoff's second law.[2]
- (b)(i)1Two batteries, each of electromotive force (e.m.f.) 6.0 V and negligible internal resistance, are connected in series with three resistors, as shown in [Figure 5.1]. Resistor X has resistance 4.0 Ω and resistor Y has resistance 1.5 Ω. The resistance R of the variable resistor is changed until the voltmeter in the circuit reads zero. Calculate 1. the current I in the circuit,[1]
- (b)(i)2Two batteries, each of electromotive force (e.m.f.) 6.0 V and negligible internal resistance, are connected in series with three resistors, as shown in [Figure 5.1]. Resistor X has resistance 4.0 Ω and resistor Y has resistance 1.5 Ω. The resistance R of the variable resistor is changed until the voltmeter in the circuit reads zero. Calculate 2. the resistance R.[2]
- (b)(ii)Resistors X and Y are wires made from the same material. The diameter of the wire of X is twice the diameter of the wire of Y. Determine the ratio average drift speed of free electrons in X / average drift speed of free electrons in Y.[2]
- (b)(iii)The resistance R of the variable resistor is now increased. State and explain the effect of the increase in R on the power transformed by each of the batteries.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2018). The mark or mark type is shown in brackets.
- [M1] sum of e.m.f.(s) = sum of p.d.(s)
- [A1] around a loop / around a closed circuit
- [A1] 6.0 – 4.0I = 0
- I = 1.5 A
- [C1] 6.0 + 6.0 = I (4.0 + R + 1.5)
- 12 = 1.5 (4.0 + R + 1.5)
- [A1] R = 2.5 Ω
- or 6.0 = I (R + 1.5)
- 6.0 = 1.5 (R + 1.5)
- (C1)
- (A1)
- or combines 6 = 4I and 6 = I(R + 1.5) to give
- 4 = R + 1.5
- (C1)
- (A1) R = 2.5 Ω
- [C1] I = Anvq
- ratio = 1^2 / 2^2
- [A1] = 0.25
- [B1] total (circuit) resistance increases
- [M1] current / I decreases or P ∝ I or P ∝ 1 / (total resistance)
- [A1] power (transformed) decreases
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