A circuit is constructed with four resistors, one capacitor, one battery and a s

Question

A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 56 , R3= 45 and R4 = 131 . The capacitance is C = 69 F and the battery voltage is V = 24 V.

1)

The switch has been open for a long time when at time t = 0, the switch is closed. What is I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?A

You currently have 0 submissions for this question. Only 10 submission are allowed.
You can make 10 more submissions for this question.

2)

What is I1(), the magnitude of the current that flows through the resistor R1 a very long time after the switch has been closed?A

You currently have 0 submissions for this question. Only 10 submission are allowed.
You can make 10 more submissions for this question.

3)

What is Q(), the charge on the capacitor after the switch has been closed for a very long time?C

You currently have 0 submissions for this question. Only 10 submission are allowed.
You can make 10 more submissions for this question.

4)

Consider the circuit above, with R5 = 121 in series with the capacitor. Once again, the switch has been open for a long time when at time t = 0, the switch is closed. What is I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?A

You currently have 0 submissions for this question. Only 10 submission are allowed.
You can make 10 more submissions for this question.

5)

Continuing with the new circuit, what is Q(), the charge on the capacitor after the switch has been closed for a very long time?

C

Explanation / Answer

R1 = R2 = 56

R3= 45 and R4 = 131 . capacitance is C = 69 F battery voltage is V = 24 V.

1.We should consider the capacitor to be in the "discharged" state just prior to t=0.So the voltage across it is 0V. This causes R2 to be in parallel with R3. It is in series then with R1 and R4.

Current,I total = I1 = V (R1+R4+(R2 || R3))

        I1 = 24 (56+131+(56 || 45))

I1=0.113 A

(2) The capacitor, at t=infinity has no more currents leaving or arriving as everything has reached equilibrium by then. The current at R2 is also zero. It has no voltage drop. Without current through R2 and C, the capacitor can be simply removed without affecting the circuit .

Itotal = I1 = I3 = I4 = V (R1+R3+R4)

        I3 = 24V (56+45+131)

        I3=0.103 A

3)The voltage drop across R3 will be the voltage across C:

V3 = I3 R3 = 4.65 V

4) R5 = 121

Uncharged capacitors are modeled as short circuits at t=0

The resistance seen by the source = R3+R2||R5+(R1+R4)=45+56||121+(56+131)=270.28

I1(0) = 24/270.28= 0.088 A

5) Continuing with the new circuit, what is Q( infinity), the charge on the capacitor after the switch has been closed for a very long time

A charged capacitor is modeled as an open circuit

Vc = 24/(56+56+45+131) * (56+45) = 8.4167 V

Q = C*V = 69*10-6*8.4167 = 5.8*10-4 C

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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