Consider the circuit shown in the figure below. (Assume R1 = 12.0 , R2 = 1.95 ,
ID: 1491787 • Letter: C
Question
Consider the circuit shown in the figure below. (Assume R1 = 12.0 , R2 = 1.95 , and V = 6.10 V.)
(a) Calculate the equivalent resistance of the R1 and 5.00- resistors connected in parallel. ________
(b) Using the result of part (a), calculate the combined resistance of the R1, 5.00- and 4.00- resistors. ________
(c) Calculate the equivalent resistance of the combined resistance found in part (b) and the parallel 3.00- resistor. _______
(d) Combine the equivalent resistance found in part (c) with the R2 resistor. _____
(e) Calculate the total current in the circuit. ________A
(f) What is the voltage drop across the R2 resistor? ______ V
(g) Subtracting the result of part (f) from the battery voltage, find the voltage across the 3.00- resistor. ______ V
(h) Calculate the current in the 3.00- resistor.
_________A
Explanation / Answer
R1 = 12.0
R2 = 1.95
V = 6.10 V
(a) The equivalent resistance of the R1 and 5.00- resistors connected in parallel R = ?
We know (1/R ) = (1/R1)+(1/5)
= (1/12)+(1/5)
= 0.2833
R = 1/0.2833
= 3.529
(b) the combined resistance of the R1, 5.00- and 4.00- resistors R ' = R + 4 = 3.529 + 4 = 7.529
(c) the equivalent resistance of the combined resistance found in part (b) and the parallel 3.00- resistor,R "= ?
We know (1/R") =(1/R') +(1/3)
=(1/7.529)+(1/3)
= 0.4661
R"= 1/0.4661
= 2.145
(d) the equivalent resistance found in part (c) with the R2 resistor Rq = R" + R2
= 2.145 +1.95
= 4.095
(e) the total current in the circuit i = V/Rq
= 6.1 /4.095
= 1.489 A
(f) the voltage drop across the R2 resistor is V' = iR2
=1.489 (1.95)
= 2.904 volt
(g) Subtracting the result of part (f) from the battery voltage,
Voltage across remaing circuit is V " = V - V ' = 6.1 volt - 2.904 volt
= 3.195 volt
the voltage across the 3.00- resistor is V " = 3.195 volt
(h) the current in the 3.00- resistor i ' = V"/3
= 3.195 /3
= 1.065 A