Consider the circuit shown in the figure below. (Assume R 1 = 12.0 , R 2 = 1.95
ID: 1402211 • Letter: C
Question
Consider the circuit shown in the figure below. (Assume R1 = 12.0 , R2 = 1.95 , and V = 6.85 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
here,
R1 = 12 ohm
R2 = 1.95 ohm
V = 6.85 V
(a)
the equivalent resistance of the R1 and 5.00- resistors connected in parallel, R1'
R1' = R1 * 5/(R1 + 5)
R1' = 12 * 5/(12 + 5)
R1' = 3.53 ohm
the equivalent resistance of the R1 and 5.00- resistors connected in parallel is 3.53 ohm
(b)
the R1' and 4 ohm resistance are in series,
their equivalent resistance , Re' = R1' + 4 ohm
Re' = 7.53 ohm
the combined resistance of the R1, 5.00- and 4.00- resistors is 7.53 ohm
(c)
the Re' and 3 ohm resistance are in parallel,
their equivalent resistance , R2' = Re' * 3 /(Re' +3)
R2' = 2.15 ohm
the equivalent resistance of the combined resistance found in part (b) and the parallel 3.00- resistor is 2.15 ohm
(d)
as R2' and R2 are in series ,
their equivalent resistance , Req = R2 + R2'
Req = 1.95 + 2.15
Req = 4.1 ohm
the equivalent resistance found in part (c) with the R2 resistor is 4.1 ohm