The figure shows a circuit of four resistors that are connected to a larger circ

Question

The figure shows a circuit of four resistors that are connected to a larger circuit. The graph below the circuit shows the electric potential V(x) as a function of position x along the lower branch of the circuit, through resistor 4; the potential VA is 11.4 V. The graph above the circuit shows the electric potential V(x) versus position x along the upper branch of the circuit, through resistors 1, 2, and 3; the potential differences are ?VB = 2.32 V and ?VC = 4.54 V. Resistor 3 has a resistance of 232 ?. What is the resistance of (a) resistor 1 and (b) resistor 2?

Explanation / Answer

Using Kirchhoff's loop rule, the sum of the voltage drops in theloop R1,R2,R3,R4 willbe zero.
So
?VB + ?VC + ?VD =VA
?VD=4.56 V
where I define ?VD as the voltage drop acrossR3 . The voltage drop across R4 is-VA as can be seen in the second graph. There is a minussign as we are going the opposite direction across R4.

The current going thru R1,R2, andR3 is the same, let's call it I1 .

Using Ohm's Law, we can find I1 as
?VD =I1R3
4.56=I1.232
I1=1.97 * 10-2
and then Ohm's Law again to find
R1 = ?VB/I1
R1 = 118.035 ?

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.