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In a transistor circuit shown in figure, if the base current is $35\mu A$, then the value of resistor ${R_b}$ is,
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A. $257k\Omega $.
B. $123.5k\Omega $.
C. $380.05k\Omega $.
D. None of these.

Last updated date: 13th Jun 2024
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Hint:Kirchhoff's loop rule states that, in a closed circuit, the sum of all the voltages is equal to zero. The sign while applying the Kirchhoff’s loop rule depends upon the direction in which we move while considering all the voltages.

Step by step solution:
Step 1.
It is given that the base current is $35\mu A$ in the above circuit and the battery is of$9V$.
Step 2.
Apply Kirchhoff’s rule in the circuit above,
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Here the direction is along the flow of current; therefore there will be voltage drop as current flows from high voltage towards low voltage. The sum of
According to Kirchhoff’s rule,
  9 - \left( {{I_b} \cdot {R_b}} \right) = 0 \\
  {I_b} \cdot {R_b} = 9 \\
 \]………eq. (1)
Step 4.
Given that the base current${I_b} = 35\mu A$,
Replace ${I_b} = 35\mu A$ in the equation (1).
\[{I_b} \cdot {R_b} = 9\]
Put,${I_b} = 35\mu A$,
  {I_b} \cdot {R_b} = 9 \\
  {R_b} = \dfrac{9}{{{I_b}}} \\
  {R_b} = \dfrac{9}{{35 \times {{10}^{ - 6}}}} \\
  {R_b} = 257.143 \times {10^3}\Omega \\
  {R_b} \approx 257k\Omega \\
So, the value of \[{R_b} = 257k\Omega \] when base current is ${I_b} = 35\mu A$.

The correct answer is option A.

Additional information:A transistor is a semiconductor device which can be used to amplify or switch electronic signals and electrical power. It has three terminals. A semiconductor is neither a conductor or an insulator, a semiconductor is a poor conductor but after doping they become a conductor. The doping results in two types of semiconductors namely p-type and n-type. A p-type semiconductor is formed when a trivalent impurity is added to an intrinsic semiconductor whereas in n-type semiconductor the pentavalent impurities are added to the intrinsic semiconductor.

While applying Kirchhoff’s rule students should remember that if we are following the direction of flow of current then there will be voltage drop as current flows from high voltage to low voltage. Also it is advisable for students to remember the concept of Kirchhoff’s junction rule because it can help students to find the unknown voltage in the closed circuit or the unknown current in the closed circuit. Always remember that the Kirchhoff’s junction rule is applied only if the circuit is closed.