A student analysed the simple d.c

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Circuits · Electric Circuits

Problem

A student analysed the simple d.c. network described below and recorded the indicated values of current and potential difference. • At junction J, the student marked the currents as:

I_1 = 3\,\text{A}

entering,

I_2 = 1\,\text{A}

leaving,

I_3 = 0.5\,\text{A}

entering and

I_4 = 1.5\,\text{A}

leaving. • In one rectangular loop of the same circuit the student wrote: a

12\,\text{V}

battery (rise), a

4\,\Omega

resistor with

1.5\,\text{A}

(drop

=6\,\text{V}

), and a

2\,\Omega

resistor with

2\,\text{A}

(drop

=4\,\text{V}

). (i) Examine the current values at junction J and state, with reason, whether the student’s assignment satisfies Kirchhoff’s current law. (ii) If the assignment is incorrect, determine the algebraic condition that must be satisfied at the junction and suggest one possible corrected value of any one current that would restore consistency. (iii) Using the figures given for the loop, verify whether the student’s recorded voltages satisfy Kirchhoff’s voltage law. Show the algebraic sum explicitly. (iv) Identify the single sign-convention error (current direction or voltage rise/drop) that is most likely responsible for any violation found in part (iii).

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