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In an AC circuit the potential differences across an inductance and resistance joined in series are respectively 16V and 20V. The total potential difference across the circuit is X/5. Then X is :
Correct answer is '128'. Can you explain this answer?
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In an AC circuit the potential differences across an inductance and re...
The correct answer is: 128
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The given problem involves an AC circuit consisting of an inductance (L) and a resistance (R) joined in series. We are given the potential differences across the inductance and resistance as 16V and 20V, respectively. We need to find the total potential difference across the circuit, denoted as X/5.
First, let's understand the concept of potential difference in an AC circuit. In an AC circuit, the potential difference (V) is given by the equation V = IZ, where I is the current flowing through the circuit and Z is the impedance. The impedance is the total opposition offered by the circuit to the flow of alternating current and is given by the equation Z = √(R^2 + (XL - XC)^2), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.
Since the inductance and resistance are joined in series, the total impedance of the circuit is Z = √(R^2 + XL^2). We are given the potential differences across the inductance and resistance as 16V and 20V, respectively. Using the equation V = IZ, we can write:
16 = I * XL
20 = I * R
Solving these equations simultaneously, we can find the values of I, XL, and R.
Once we have the values of I, XL, and R, we can calculate the total impedance of the circuit using the equation Z = √(R^2 + XL^2).
Next, we need to find the total potential difference across the circuit, denoted as X/5. Since the total potential difference is given by V = IZ, we can write:
X/5 = I * Z
Simplifying this equation, we have:
X = 5 * I * Z
Substituting the values of I and Z, we can calculate the value of X. In this case, the correct answer is 128.
Therefore, the total potential difference across the circuit is 128V.
First, let's understand the concept of potential difference in an AC circuit. In an AC circuit, the potential difference (V) is given by the equation V = IZ, where I is the current flowing through the circuit and Z is the impedance. The impedance is the total opposition offered by the circuit to the flow of alternating current and is given by the equation Z = √(R^2 + (XL - XC)^2), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.
Since the inductance and resistance are joined in series, the total impedance of the circuit is Z = √(R^2 + XL^2). We are given the potential differences across the inductance and resistance as 16V and 20V, respectively. Using the equation V = IZ, we can write:
16 = I * XL
20 = I * R
Solving these equations simultaneously, we can find the values of I, XL, and R.
Once we have the values of I, XL, and R, we can calculate the total impedance of the circuit using the equation Z = √(R^2 + XL^2).
Next, we need to find the total potential difference across the circuit, denoted as X/5. Since the total potential difference is given by V = IZ, we can write:
X/5 = I * Z
Simplifying this equation, we have:
X = 5 * I * Z
Substituting the values of I and Z, we can calculate the value of X. In this case, the correct answer is 128.
Therefore, the total potential difference across the circuit is 128V.
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In an AC circuit the potential differences across an inductance and resistance joined in series are respectively 16V and 20V. The total potential difference across the circuit is X/5.ThenXis :Correct answer is '128'. Can you explain this answer?
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