Consider the circuit shown in the figure below. (Assume R1 = 6.00 , R2 = 2.20 ,
ID: 1502067 • Letter: C
Question
Consider the circuit shown in the figure below. (Assume R1 = 6.00 , R2 = 2.20 , and V = 12.00 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
a) equivallent resistance = R1*5.00/(R1+5.00) = 6*5/11 = 2.727 ohm
b) combined resistance, Rc = 2.727 + 4.00 = 6.727 ohm
c) equivallent resistance Req= Rc*3.00/(Rc+3.00) = 6.727*3.00/9.727 = 2.074 ohm
d) combined resistance Rcom= Req+R2 = 2.074 + 2.20 = 4.274 ohm
e) total current , i = 12.00/(Rcom) = 12.00/(4.274) = 2.807 A
f) voltage drop across R2 = R2*i = 2.20*2.807 = 6.175 v
g) after subtraction remaining voltage = 12.00 - 6.175 = 5.824 v = voltage across 3.00 ohm resistor
h) current in hte 3.00 ohm resistor = 5.824/3.00 = 1.941 A