The principles of conservation of which two quantities are associated with Kirchhoff’s first and second laws?
| first law | second law | |
|---|---|---|
| (A) | charge | energy |
| (B) | charge | voltage |
| (C) | energy | charge |
| (D) | voltage | charge |
Correct Answer: \( \boxed{\mathrm{A}} \)
Kirchhoff’s first law is based on the conservation of charge.
Kirchhoff’s second law is based on the conservation of energy.
Therefore, the correct answer is (A).
The diagram shows the currents in part of an electric circuit.
The resistors are identical.
Which equation is not correct?
Correct Answer: \( \boxed{\mathrm{C}} \)
Applying Kirchhoff’s current law at the lower junction gives
\( I_3=I_4+I_5 \).
At the upper junction,
\( I_1=I_2+I_3 \).
Hence, \( I_2=I_1-I_3 \), and since \( I_3=I_4+I_5 \), option (A) is also correct.
Option (C) incorrectly states \( I_2=I_3+I_4+I_5 \), which does not satisfy Kirchhoff’s current law.
Therefore, the correct answer is (C).
A battery of electromotive force (e.m.f.) \(6.0\,\mathrm{V}\) and negligible internal resistance is connected to three resistors, as shown.
The current in the battery is \(0.12\,\mathrm{A}\).
What is resistance \(R\)?
Correct Answer: \( \boxed{\mathrm{B}} \)
The total resistance of the circuit is
\( R_{\text{total}}=\dfrac{V}{I}=\dfrac{6.0}{0.12}=50\,\Omega \)
The \(30\,\Omega\) resistor is in series with the parallel combination of \(60\,\Omega\) and \(R\).
Hence, the equivalent resistance of the parallel section is
\( R_{\text{parallel}}=50-30=20\,\Omega \)
Using the parallel resistance formula,
\( \dfrac{1}{20}=\dfrac{1}{60}+\dfrac{1}{R} \)
\( \dfrac{1}{R}=\dfrac{1}{20}-\dfrac{1}{60}=\dfrac{1}{30} \)
\( R=30\,\Omega \)
Therefore, the correct answer is (B).
