(a) State two essential differences between a moving coil galvanometer and a d.c. generator.
(b) Explain the term eddy currents and state two devices in which the currents are applied.
(c) State the principle on which the potentiometer is based when it is functioning.
(d) A source of e.m.f. 110 V and frequency 60Hz is connected to a resistor, an inductor and a capacitor in series. When the current in the capacitor is 2A, the potential differences across the resistor is 80 V and that across the inductor is 40 V. Draw the vector diagram of the potential differences across the inductor, the capacitor and the resistor.
Calculate the:
(i) potential difference across the capacitor;
(ii) capacitance of the capacitor;
(iii) inductance of the inductor. [π = 3.14]
(b) Explain the term eddy currents and state two devices in which the currents are applied.
(c) State the principle on which the potentiometer is based when it is functioning.
(d) A source of e.m.f. 110 V and frequency 60Hz is connected to a resistor, an inductor and a capacitor in series. When the current in the capacitor is 2A, the potential differences across the resistor is 80 V and that across the inductor is 40 V. Draw the vector diagram of the potential differences across the inductor, the capacitor and the resistor.
Calculate the:
(i) potential difference across the capacitor;
(ii) capacitance of the capacitor;
(iii) inductance of the inductor. [π = 3.14]
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Correct Answer: Option
Explanation:
a) Differences between a d. c. generator and a moving coil galvanometer.
(b) Eddy currents are currents induced in a conductor when subjected to varying magnetic field.
Any valid additional information e.g.
eddy current flows in a circular path or closed loops;
eddy current generates heat;
eddy current cannot flow through gaps or slots;
The currents move in such a direction as to oppose the change producing them.
Devices in which eddy currents are applied
pointers of sensitive electric meters
sensitive mass balances
brakes in large electric motors
speedometers in automobiles
detection of cracks in railway tracks
detection of metals
(c) Principle on which a potentiometer is based
When a steady current is allowed to pass through a uniform wire, equal lengths of the wire will have equal potential differences.
OR
The p.d across a length of a wire is (directly) proportional to the length provided the wire has a uniform cross section.
(d)
Vector diagram showing
V\(_L\) with arrow
V\(_C\) with arrow
V\(_R\) with arrow
(i) V\(^2\) = V\(_R^2\) + (V\(_L\) - V\(_C\))\(^2\)
110\(^2\) = 80\(^2\) + (40 – V\(_C\))\(^2\)
(40 – V\(_C\)) = \(\sqrt{(110 + 80) (110 – 80)}\)
40 – V\(_C\) = + 75.5
V\(_C\) = 40 + 75.5
V\(_C\) = 115.5V
(ii) X\(_c\) \(\frac{V_c}{I} = \frac{1}{2 \pi f c}\)
C = \(\frac{1}{2 \pi fV_c}\)
C \(\frac{2}{2 \times 3.14 \times 60 \times 115.5} = 45.9\muF\)
(iii) \(V_L = IX_L = I \times 2 \pi fL}\)
L = \(\frac{V_l}{I \times 1 \times 2 \pifVc}\)
C = \(\frac{2}{2 \times 3.142 \times 60 \times 2}\)
= 0.053H
a) Differences between a d. c. generator and a moving coil galvanometer.
| D. C. generator | moving coil galvanometer |
| converts mechanical energy to electrical energy | converts electrical energy to mechanical energy. |
| uses split rings or commutator | uses hair springs. |
| rotation of coil is continuous | rotation of coil is incomplete |
| uses carbon brushes (as terminals) | uses jeweled bearings (as terminals) |
(b) Eddy currents are currents induced in a conductor when subjected to varying magnetic field.
Any valid additional information e.g.
eddy current flows in a circular path or closed loops;
eddy current generates heat;
eddy current cannot flow through gaps or slots;
The currents move in such a direction as to oppose the change producing them.
Devices in which eddy currents are applied
pointers of sensitive electric meters
sensitive mass balances
brakes in large electric motors
speedometers in automobiles
detection of cracks in railway tracks
detection of metals
(c) Principle on which a potentiometer is based
When a steady current is allowed to pass through a uniform wire, equal lengths of the wire will have equal potential differences.
OR
The p.d across a length of a wire is (directly) proportional to the length provided the wire has a uniform cross section.
(d)
Vector diagram showing
V\(_L\) with arrow
V\(_C\) with arrow
V\(_R\) with arrow
(i) V\(^2\) = V\(_R^2\) + (V\(_L\) - V\(_C\))\(^2\)
110\(^2\) = 80\(^2\) + (40 – V\(_C\))\(^2\)
(40 – V\(_C\)) = \(\sqrt{(110 + 80) (110 – 80)}\)
40 – V\(_C\) = + 75.5
V\(_C\) = 40 + 75.5
V\(_C\) = 115.5V
(ii) X\(_c\) \(\frac{V_c}{I} = \frac{1}{2 \pi f c}\)
C = \(\frac{1}{2 \pi fV_c}\)
C \(\frac{2}{2 \times 3.14 \times 60 \times 115.5} = 45.9\muF\)
(iii) \(V_L = IX_L = I \times 2 \pi fL}\)
L = \(\frac{V_l}{I \times 1 \times 2 \pifVc}\)
C = \(\frac{2}{2 \times 3.142 \times 60 \times 2}\)
= 0.053H