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Circuits and Kirchhoff's laws questions
Every circuit rule you have ever used comes out of two conservation laws. Charge is conserved at every junction. Energy is conserved round every loop. Series, parallel and power all follow from those two sentences.
20 original questions · 60 marks · the circuits and kirchhoff's laws notes · Electricity
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State Kirchhoff's first law and the conservation principle it expresses.
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The sum of the currents into a junction equals the sum of the currents out of it (1). This expresses conservation of charge (1).Two resistors of 20 Ω and 30 Ω are connected in series. Calculate the total resistance.
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In series resistances add: R = 20 + 30 (1)
R = 50 Ω (1)Two 20 Ω resistors are connected in parallel. Calculate the total resistance.
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1/R = 1/20 + 1/20 (1)
R = 10 Ω (1)Two 1.5 V cells are connected in series to form a battery. State the emf of the battery. State the emf if the two identical cells are instead connected in parallel, and give one advantage of the parallel arrangement.
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Series: emf = 1.5 + 1.5 = 3.0 V (1). Parallel: emf = 1.5 V, and the cells share the current between them, so each works less hard and the battery lasts longer (1).Explain why the combined resistance of two resistors in parallel is always less than the smaller of the two resistances.
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Adding a resistor in parallel adds an extra path for current without removing any (1). For the same pd the total current is therefore larger, so the combined resistance V/I is smaller than that of either branch alone (1).State which form of the power equation is most direct for comparing the powers dissipated in two resistors in series, and give the reason.
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P = I2R (1), because components in series share the same current (1).A 6.0 Ω resistor and a 3.0 Ω resistor are connected in parallel across a 12 V supply. Calculate (a) the total resistance and (b) the total current from the supply.
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(a) 1/R = 1/6.0 + 1/3.0 (1)
R = 2.0 Ω (1)
(b) I = V/R = 12/2.0 = 6.0 A (1)A 4.0 Ω and an 8.0 Ω resistor are connected in series across a 12 V supply. Calculate (a) the current in the circuit and (b) the potential difference across each resistor.
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(a) R = 4.0 + 8.0 = 12 Ω (1)
I = 12/12 = 1.0 A (1)
(b) V1 = IR1 = 4.0 V (1)
V2 = IR2 = 8.0 V (1)At a junction in a circuit, currents of 3.0 A and 2.0 A flow in, and a single wire carries the current out. Determine the current in the output wire, stating the law you use.
A resistor of 5.0 Ω carries a current of 2.0 A. Calculate the power dissipated in it.
An electric shower is rated 10.5 kW at 230 V. Calculate the current it draws and the resistance of its heating element.
A phone charger's packaging claims it delivers 38 kJ of energy in a 45 minute charge. In a test it supplies a steady 2.1 A at 5.0 V for the full 45 minutes. Deduce whether the claim is accurate.
A battery of emf 24 V drives a current round a series loop containing three components. The pds across two of them are 9.0 V and 7.5 V. Determine the pd across the third component, stating the law you use.
A camping heater runs from a 12 V supply of negligible internal resistance and has two identical 4.6 Ω elements. Calculate the total power when the elements are connected (a) in series and (b) in parallel.
A 4.0 Ω resistor is connected in series with a parallel combination of a 6.0 Ω and a 3.0 Ω resistor, across a 12 V supply. Calculate (a) the total resistance, (b) the total current and (c) the current in each of the parallel resistors.
A 60 W lamp is switched on for 5.0 minutes while connected to a 230 V supply. Calculate (a) the energy it transfers and (b) the charge that flows through it.
State Kirchhoff's second law and the conservation principle it expresses.
A car's two headlamps, each of resistance 6.0 Ω, are connected in parallel. The pair is in series with wiring of total resistance 0.40 Ω across the car's 12 V supply. The circuit is protected by a 5.0 A fuse. Deduce whether the fuse melts when both headlamps are on.
A 3.0 Ω resistor and a 9.0 Ω resistor are connected in series across a 6.0 V supply of negligible internal resistance. Calculate the power dissipated in each resistor, and state which runs hotter.
Two identical filament lamps are connected to a battery of negligible internal resistance, first in series and then in parallel. Explain fully why the lamps are brighter in parallel, and why the battery discharges sooner. A student claims that each lamp in series dissipates exactly one quarter of its parallel power. Comment on that claim.
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