AP® Physics C: E&M -Kirchhoff’s Junction Rule - MCQs
Questions
The figure above represents a section of a circuit containing three resistors, X, Y, and Z, of different sizes but made of the same material. Which of the following correctly ranks the current in the resistors?
(A)\(I _{z}\)> \(I_{x}\)> \(I_{y}\)
(B)\(I _{z}\)= \(I_{x}\)> \(I_{y}\)
(C)\(I _{z}\)= \(I_{x}\)=\( I_{y}\)
(D)\(I _{y}\)>\( I_{x}\)> \(I_{z}\)
▶️Answer/Explanation
Ans: D
This option is correct. Current is proportional to the cross sectional area of the conductor and inversely proportional to length of the conductor. Conductors X and Y have the same cross sectional area and Y has clearly the smaller length. Conductors X and Z have the same length, but X has a larger cross sectional area. This leads to the conclusion that \(I _{y}\)>\(I_{x}\)> \(I_{z}\) .
Questions
In the circuit shown above, the current through the ammeter is 20 mA and the voltmeter indicates 1.0 V. The resistance of resistor R is most nearly
(A) 50 W
(B) 33 W
(C) 20 W
(D) 14 W
▶️Answer/Explanation
Ans: B
This option is correct. The voltage across the parallel multi branch section to the right of resistor R is 1.0 Volt, the same as the measurement on the voltmeter. Since the two 20 ohm resistors are in equivalent positions, they share equally the remaining 2 volts supplied by the battery. This means that the net resistance of the rest of the circuit must also be 20 ohms. The equivalent resistance of the section of the circuit to the right of R is 50 ohms — added in “parallel” to the unknown resistor must give 20 ohms. The value that will give 20 ohms is 33.3 ohms { \(\frac{1}{33.3}+\frac{1}{50}=\frac{1}{20}\)}.
Questions
In the circuit shown above, the current through the ammeter is 20 mA and the voltmeter indicates 1.0 V. What is the current through the 40 W resistor?
(A) 7.5 mA
(B) 10 mA
(C) 20 mA
(D) 40 mA
▶️Answer/Explanation
Ans: C
This option is correct. The 40 ohm resistor and the ammeter are located in equivalent positions in the circuit. No matter what the direction of current through the ammeter, it will split at one of the junctions on either side of the ammeter, and recombine when it reaches the corresponding junction on either side of the 40 ohm resistor. So the 40 ohm resistor also has a current of 20 mA.