DC Circuit Analysis Questions and Answers

Answer: B

The voltage drop is 1.0 V. By Ohm's law the voltage across a resistor is the product of the current and the resistance, with the current of 20 mA written as 0.02 A.

\[ V = IR = 0.02 \times 50 = 1.0\ \text{V} \]

The value 0.1 V would come from 2 mA, 10 V from 200 mA, and 100 V from 2 A, so those options correspond to wrong currents. The second option is the answer.

Answer: C

The current I1 is 1.0 A. By Kirchhoff's current law, the sum of the currents entering a junction equals the sum of the currents leaving it. In the figure, I1 and I2 flow into the junction, while I3, I4 and I5 flow out.

\[ I_1 + I_2 = I_3 + I_4 + I_5 \]

\[ I_1 + 0.5 = 1.5 \Rightarrow I_1 = 1.0\ \text{A} \]

The value 0 A would need no current at all, 0.5 A would make the junction currents unequal (1.0 in, 1.5 out), and 1.5 A would be the total leaving the junction and not the value of I1 alone. So the third option is the answer.

Answer: A

R_DC is 6 Ω. A Wheatstone bridge is balanced when the ratio of the resistances in one arm equals the ratio in the other, so the products of opposite arms are equal. With P in AB and Q in BC, S in AD and R in DC:

\[ \frac{P_{AB}}{Q_{BC}} = \frac{S_{AD}}{R_{DC}} \]

\[ \frac{500}{250} = \frac{12}{R_{DC}} \]

\[ R_{DC} = 6\ \Omega \]

The value 24 Ω is what one gets by taking the ratio the wrong way round, and 12 Ω and 48 Ω do not satisfy the balance condition. The first option is correct.

Answer: D

The resistance increases 12 times. The resistance of a wire is R = ρL/A, and its area depends on the square of the diameter. When the length becomes 3L and the diameter becomes d/2, the area becomes one fourth.

\[ R' = \frac{\rho (3L)}{A/4} = 12\,\frac{\rho L}{A} = 12R \]

A longer wire increases the resistance (by 3 times) and a thinner wire increases it again (by 4 times), so the effect is multiplied, 3 x 4 = 12, and it cannot decrease. So the fourth option is correct.

Answer: A

The liquid or solution that undergoes a chemical change on the passage of an electric current is called an electrolyte. Examples are acidified water, copper sulphate solution and molten salts, which contain ions that carry the current and are discharged at the electrodes.

The anode and cathode are the electrodes, the positive and negative plates dipped in the electrolyte, and an ion is a charged particle. They are not the liquid in which the change occurs, so the first option is correct.

Answer: C

By Faraday's first law of electrolysis, the mass of a substance liberated or deposited at an electrode is directly proportional to the quantity of charge passed, which is the current multiplied by time, so it is directly proportional to the time for which the current is passed.

\[ m = Z\,I\,t \]

The mass is not inversely proportional to the time or to the current, and it is not independent of the time, because a longer current deposits more material. So the third option is correct.

Answer: D

An automobile ignition battery is not an application of a mercury cell. Mercury cells give a very steady voltage at a small current and are made in small button sizes, so they are used in digital watches, calculators and hearing aids.

A car's ignition and starting need a large current for a short time, which is the job of a lead-acid secondary battery. So the fourth option is the answer.

Answer: C

'Rechargeable' is not a characteristic of a primary cell. A primary cell is used once and then thrown away, because its chemical reaction cannot be reversed by passing a current back. Rechargeable cells are secondary cells.

A primary cell is cheaper than a secondary cell, light in weight, and gives a small voltage and current, as the other options say. So the third option is the one that is not a characteristic.

Answer: B

The bending of the electrodes (plates) due to overcharging, discharging, an improper electrolyte or temperature is called buckling. The plates swell and bend as a result of the unequal chemical changes and heat in the cell.

Sulphation is the formation of hard lead sulphate crystals on the plates of a battery that is left discharged, trickle charging is a slow charge to keep a cell full, and polarization is the formation of gas bubbles on the plates in a cell. So the second option is the answer.

Answer: A

The arrangement needs 8 cells in series and 4 parallel rows. Each cell gives 1.5 V, so to get 12 V the number of cells in series is 12/1.5 = 8. Each cell has a capacity of 2 AH, so for a capacity of 8 AH the number of parallel rows is 8/2 = 4.

\[ \frac{12}{1.5} = 8, \qquad \frac{8}{2} = 4 \]

That gives 8 x 4 = 32 cells in all. The option '4, 8' reverses the numbers and would give 6 V, '6, 6' would give 9 V and a capacity of 12 AH, and '8, 8' would give the right voltage but a capacity of 16 AH, which is more than needed. So the first option is correct.