Tim Cinel

Reference directions of currents and numerical values, Kirchhoff’s Current Law

Q1

With the reference directions of currents shown in Fig.Q1, calculate the

numerical values of the missing current I1: (Ans: 2 A, 6 A, -2 A)

a) Outgoing = 0 -6 -4 + 8 + I = 0 2 = I

b) Outgoing = 0 15 – 7 -2 -I = 0 I = 6

c) Outgoing = 0 -6 - 4 + 12 + I = 0 I = -2

Q2

Mark the reference direction and calculate the numerical values of the

missing currents in the following parts of circuits in Fig.Q2:

(Ans (a) 8 A, 5 A, 7 A, 4 A, (b) 6 mA, 3 mA, 5 mA )

I1 = 18 – 10 I1 = 8A

I2 = I1 – 3 I2 = 5A

I3 = I2 + 2 I3 = 7A

I4 = I3 – 3 I4 = 4A

I1 = 10 – 4 I1 = 6mA

I2 = 15 – 10 – 2 I2 = 3mA

I3 = 2 + 3 I3 = 5mA

Kirchhoff’s Voltage Law

Q3

With the voltage polarity marked in the circuits below, calculate the

numerical values of the unknown voltages:

(Ans: (a) 42 V, -28 V, (b) 14 V (c) 8 V, 6 V, 4 V)

Leaving = 0 -24 – 18 + V1 = 0 V1 = 42V

Leaving = 0 +10 + 18 + V2 = 0 V2 = -28

V₁ = 42V

V₂ = -28

V = 42 – 28

V = 14V

-12 + 6 – 2 + V1 = 0 V1 = 8V

-12 + 6 + V2 = 0 V2 = 6V

-12 + 8 + V3 = 0 V3 = 4V

Resistor

Q1

A resistor is being tested using the circuit shown in Fig.Q1 in which a variable dc power

supply delivers current to the resistor.

(a) With one setting of the power supply the ammeter reads 2 mA while the voltmeter reads 4.4 V. Calculate the resistance.

R = 2.2 kΩ

(b) The current is then increased to 5 mA. What is the expected voltmeter reading?

(Ans: (a) 2.2 kΩ, (b) 11 V)

V = 11V

Q2

In the circuit shown in Fig.Q1, (a) calculate the power dissipated in the same 2.2 kΩ

resistor when the ammeter reads 2 mA.

W = 8.8mW

(b) If the resistor power rating is known to be 0.25 W, what is the maximum voltage to which you can raise the supply voltage safely?

(Ans: (a) 8.8 mW, (b) 23.4 V)

Let P = 2.5*10² W

Q3

A 22 kΩ and a 2.2 kΩ resistor are connected in series and are used as voltage divider in the circuit shown in Fig.Q3. Both resistors have the same power rating of 0.25 W.

(a) When the supply voltage is 50 V, what are the ammeter and voltmeter readings?

(b) Can you raise the supply voltage to 100 V safely? If not, why?

22 Ohm Power > 0.25 W

What is the highest voltage to which the supply voltage can be raised?

(Ans: (a) 2.1 mA, 4.5 V, (b) No, 22 kΩ overheats (c) 81.5 V)

Q4

A 24 kΩ, 0.25 W and a 56 kΩ, 0.25 W resistor are connected in parallel as in the circuit shown in Fig.Q4.

(a) The power supply voltage is adjusted to 42 V. What are the expected readings of V, A1, A2 & A3?

(b) What is the highest voltage to which the supply voltage can be raised?

V_max = 77.5 V

(Ans: (a) 42 V, 1.75 mA, 0.75 mA & 2.5 mA (b) 77.5 V)

Tags: Circuit Theory, Physics, solution, tutorial

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