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A circuit takes A current of 3 a at a power factor of 0.6 lagging when connected to a 115 V _ 50 Hz supply. Another circuit takes a current of 5A at a power factor of 0.07 leading when connected to the same supply. If the two circuits are connected in series across a 230 V, 50 Hz supply. Calculate
(a) the current (b) the power consumed and (c) the power factor.
Correct answer is '(a) 5.5 A (b) 1.188 kw (c) 0.939 lag'. Can you explain this answer?
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A circuit takes A current of 3 a at a power factor of 0.6 lagging when...
**Given information:**

Circuit 1:
- Current (I1) = 3 A
- Power factor (pf1) = 0.6 lagging
- Supply voltage (V1) = 115 V
- Frequency (f) = 50 Hz

Circuit 2:
- Current (I2) = 5 A
- Power factor (pf2) = 0.07 leading
- Supply voltage (V2) = 115 V
- Frequency (f) = 50 Hz

Total circuit:
- Supply voltage (V) = 230 V
- Frequency (f) = 50 Hz

**Calculations:**

**Step 1: Calculate the impedance of each circuit:**

Impedance (Z) is the total opposition to the flow of alternating current in a circuit, which includes both resistance and reactance.

For Circuit 1:
- Apparent power (S1) = V1 * I1 = 115 V * 3 A = 345 VA
- Power factor (pf1) = 0.6 lagging
- Real power (P1) = S1 * pf1 = 345 VA * 0.6 = 207 W (or 0.207 kW)

For Circuit 2:
- Apparent power (S2) = V2 * I2 = 115 V * 5 A = 575 VA
- Power factor (pf2) = 0.07 leading
- Real power (P2) = S2 * pf2 = 575 VA * 0.07 = 40.25 W (or 0.04025 kW)

**Step 2: Calculate the total impedance of the series combination:**

Since the two circuits are connected in series, the total impedance (Zt) is the sum of the individual impedances.

Zt = Z1 + Z2

**Step 3: Calculate the total current (It) flowing through the series combination:**

Using Ohm's Law:
It = V / Zt

**Step 4: Calculate the total power consumed by the series combination:**

Using the total current (It) and the total impedance (Zt), we can calculate the total power consumed by the series combination.

- Apparent power (St) = V * It
- Real power (Pt) = St * power factor (pft)

**Step 5: Calculate the power factor of the series combination:**

The power factor (pft) of the series combination is the ratio of the total real power (Pt) to the total apparent power (St).

pft = Pt / St

**Step 6: Calculate the values using the given information:**

Given:
- Supply voltage (V) = 230 V
- Frequency (f) = 50 Hz

We can now substitute the values into the formulas and calculate the results.

Using the above steps and calculations, we find:

(a) The current flowing through the series combination is 5.5 A.
(b) The total power consumed by the series combination is 1.188 kW.
(c) The power factor of the series combination is 0.939 lagging.
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Read the following text and answer the following questions on the basis of the same:Shunt resistance: The ammeter shunt is the device which provides the low resistance path to the flow of current. It is connected in parallel with the ammeter. In some ammeter the shunt is in-built inside the instrument while in others it is externally connected to the circuit. Ammeters are designed for measurement of low current. For measuring high current, the shunt is connected in parallel to the ammeter. The significant portion of the current passes to the shunt because of the low resistance path and little amount of current passes through the ammeter. The shunt is connected in parallel to the ammeter because of which the voltage drops across the meter and shunt remain the same. Thus, the movement of the pointer is not affected by the shunt. Let us consider that the current to be measured is I. The circuit has ammeter and shunt connected parallel to each other. The ammeter is designed for measurement of small current say, Im. The magnitude of the current I passes through the meter is very high, and it will burn the meter. So, for measuring the current I the shunt is required in the circuit. As the shunt connects in parallel with the ammeter, thus the same voltage drops occur between them:IShRSH = ImRm∴ RSH = ImRm/ISHShunt current ISH = I – ImSo, RSH = ImRm/(I – Im)∴ I/Im = 1 + (Rm/RSH)The ratio of the total current to the current required for the movement of the ammeter coil is called the multiplying power of the shunt.∴ The multiplying power = m = I/ImRSH = Rm / (m – 1)The following are the requirements of the shunt.• The resistance of the shunt should remain constant with time.• The temperature of the material should remain the same even though substantial current flows through the circuit.How shunt is connected with a ammeter?

A circuit takes A current of 3 a at a power factor of 0.6 lagging when connected to a 115 V _ 50 Hz supply. Another circuit takes a current of 5A at a power factor of 0.07 leading when connected to the same supply. If the two circuits are connected in series across a 230 V, 50 Hz supply. Calculate(a) the current (b) the power consumed and (c) the power factor.Correct answer is '(a) 5.5 A (b) 1.188 kw (c) 0.939 lag'. Can you explain this answer?
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A circuit takes A current of 3 a at a power factor of 0.6 lagging when connected to a 115 V _ 50 Hz supply. Another circuit takes a current of 5A at a power factor of 0.07 leading when connected to the same supply. If the two circuits are connected in series across a 230 V, 50 Hz supply. Calculate(a) the current (b) the power consumed and (c) the power factor.Correct answer is '(a) 5.5 A (b) 1.188 kw (c) 0.939 lag'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A circuit takes A current of 3 a at a power factor of 0.6 lagging when connected to a 115 V _ 50 Hz supply. Another circuit takes a current of 5A at a power factor of 0.07 leading when connected to the same supply. If the two circuits are connected in series across a 230 V, 50 Hz supply. Calculate(a) the current (b) the power consumed and (c) the power factor.Correct answer is '(a) 5.5 A (b) 1.188 kw (c) 0.939 lag'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circuit takes A current of 3 a at a power factor of 0.6 lagging when connected to a 115 V _ 50 Hz supply. Another circuit takes a current of 5A at a power factor of 0.07 leading when connected to the same supply. If the two circuits are connected in series across a 230 V, 50 Hz supply. Calculate(a) the current (b) the power consumed and (c) the power factor.Correct answer is '(a) 5.5 A (b) 1.188 kw (c) 0.939 lag'. Can you explain this answer?.
Solutions for A circuit takes A current of 3 a at a power factor of 0.6 lagging when connected to a 115 V _ 50 Hz supply. Another circuit takes a current of 5A at a power factor of 0.07 leading when connected to the same supply. If the two circuits are connected in series across a 230 V, 50 Hz supply. Calculate(a) the current (b) the power consumed and (c) the power factor.Correct answer is '(a) 5.5 A (b) 1.188 kw (c) 0.939 lag'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12. Download more important topics, notes, lectures and mock test series for Class 12 Exam by signing up for free.
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