A transistor-oscillator using a resonant circuit with an inductor L (of negligible resistance) and a capacitor C in series produce oscillations of frequency f. If L is doubled and C is changed to 4C, the frequency will be :
- \(\frac{\text{f}}{4}\)
- 8f
- \(\frac{\text{f}}{2\sqrt 2}\)
- 2f
The Correct Option is C
Solution and Explanation
In a series \(LC\) circuit, frequency of \(LC\) oscillations is given by \(f=\frac{1}{2 \pi \sqrt{L C}}\) or \(f \propto \frac{1}{\sqrt{L C}}\) \(\Rightarrow \frac{f_{1}}{f_{2}}=\sqrt{\frac{L_{2} C_{2}}{L_{1} C_{1}}}\)
Given \(L_{1}=L, C_{1}=C, L_{2}=2 L, C_{2}=4 C, f_{1}=f\)
\(\therefore \frac{f}{f_{2}}=\sqrt{\frac{2 L \times 4 C}{L C}}=\sqrt{8}\) \(\Rightarrow f_{2}=\frac{f}{2 \sqrt{2}}\)
Therefore, the correct option is (C): \(\frac{\text{f}}{2\sqrt 2}\)
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Concepts Used:
Transistors
Transistor
A transistor is a type of semiconductor device that can be used to both conduct and insulate electric current or voltage. A transistor basically acts as a switch and an amplifier. In simple words, we can say that a transistor is a miniature device that is used to control or regulate the flow of electronic signals.
Parts of a Transistor:
A transistor is a combination of three terminals made of semiconducting materials that help in making a connection to an external circuit and allow current to flow. The three terminals are:
- Base: The base activates the transistor. It is thin and lightly doped. It is put in the centre of the transistor.
- Emitter: The emitter is the negative terminal of the transistor. It is heavily doped and is moderately sized.
- Collector: The collector is the negative terminal of the transistor. It is located on the right side of a transistor and is moderately doped. It is larger than the emitter.
Read More: Difference Between NPN and PNP Transistor
Types of Transistors:
A transistor is a type of electronic device which is formed by p-type and n-type semiconductors.
NPN Transistor
- NPN transistor is a type of Bipolar Junction Transistor.
- In this, electrons are major current carriers, and minor ones are holes.
- Their arrangement is in such a way that N-type doped semiconductors are separated by the layer of P-type doped semiconductors which is a thin layer of material embedded between them.
- Emitter Current = Collector Current + Base Current
PNP Transistor
- PNP transistor is also a type of Bipolar Junction Transistor.
- In these, holes are the major source that carries current, and electrons are minor.
- Their arrangement is in a way that P-type doped semiconductor is separated by N-type doped semiconductor material which is a thin layer.
- Emitter Current = Collector Current + Base Current
Read More: Characteristics of a Transistor
Configurations of a Transistor:
Using the three types of configuration can be used to design any transistor circuit. The three types of configuration of a transistor are:
- Common Emitter Transistor
- Common Base Transistor
- Common Collector Transistor
Common Emitter (CE) Configuration of a Transistor
In Common Emitter Configuration, the transistor’s emitter terminal will be connected common between the output terminal and the input terminal.
Input Characteristics
- Variation of emitter current (IB) with Base-Emitter voltage (VBE) when Collector-Emitter voltage (VCE) is held constant.
- Rin = ΔVBE/ΔIB | VCE = Constant
Output Characteristics
- Variation of collector current (IC) with Collector-Emitter voltage (VCE) when the base current (IB) is held constant.
- Rout = ΔVCE/ΔIC | IB = Constant
Current Transfer Characteristics
- The variation of the collector current (IC) with the base current (IB) when the collector-emitter voltage (VCE) is constant.
- α = ΔIC/ΔIB | VCB = Constant
Common Base (CB) Configuration of a Transistor
In Common Base Configuration, the transistor’s base terminal will be connected common between the output terminal and the input terminal.
Input Characteristics
- Variation of emitter current (IE) with Base-Emitter voltage (VBE) when the Collector Base voltage (VCB) is held constant.
- Rin = ΔVBE/ΔIE | VCB = Constant
Output Characteristics
- Variation of collector current (IC) with Collector-Base voltage (VCB) when the emitter current (IE) is held constant.
- Rout = ΔVCB/ΔIB | IE = Constant
Current Transfer Characteristics
- The variation of the collector current (IC) with the emitter current (IE) when the Collector Base voltage (VCB) is constant.
- α = ΔIC/ΔIE | VCB = Constant
Common Collector Configuration of a Transistor
In Common Collector Configuration, the transistor’s collector terminal will be connected common between the output terminal and the input terminal.
Input Characteristics
- Variation of emitter current (IB) with Collector-Base voltage (VCB) when the Collector Base voltage (VCB) is held constant.
Output Characteristics
- Variation of emitter current (IE) with Collector-Emitter voltage (VCE) when the base current (IB) is held constant.
Current Transfer Characteristics
- The variation of the collector current (IE) with the base current (IB) when the Collector-Emitter voltage (VCE) is constant.