Question

In the given circuit switch is in position a for what value of R will the circuit have a time constant of $10\mu s$.

& \left( 1 \right)2.0k\Omega \\\ & \left( 2 \right)2.5k\Omega \\\ & \left( 3 \right)1.0k\Omega \\\ & \left( 4 \right)none of these \\\ \end{aligned}$$

Answer 1

Here, in this question we are going to use a series and parallel resistance formula .There is a relationship between resistance, voltage and current. First, we will find equivalent resistance by adding when in series, and in parallel after that we will find for what value of R will the circuit have a time constant of $10\mu s$.

Complete answer:
A circuit is a visual display of current passing through wires. There are three basic types of electrical circuit such as series, parallel, series/parallel. A circuit is a complete path around which electricity flows. Battery is a must as source of electricity and the material of path of circuit must be of conductor type through which current should pass. To function a simple circuit necessary components are source of voltage, conductive path and resistor. There are two forms of electrical power used by circuits: alternating current and direct current. Every circuit has a circuit breaker which works when there is imbalanced current flow or any part of the component fails so, this failure causes damage to other components that is why circuit breaker is wired into a circuit called fuse. There is a source where electrons enter, and the place where electrons exist are called return or grounded earth.
Circuits in houses are generally wired in parallel. Resistance is the hindrance in the flow of current in the conductor. It opposes the flow of electrons. It is measured in ohms.
Italian scientist ALESSANDRO VOLTA invented the first electric circuit.
The circuit through the circuit can be found through ohm’s law and that is equal to the voltage which is divided by the resistance equivalent. And through ohm’s law we can also find potential drop across the resistor.
${{R}_{Equivalent}}=\dfrac{R\times 500}{R+500}$
$10\times {{10}^{-6}}=4\times {{10}^{-3}}\times \dfrac{R+500}{R\times 500}$
${{10}^{-2}}=4\times \dfrac{R+500}{R\times 500}$
On simplifying above equation we get:
$5R=4R+2000$
On solving the equation for fetching the value of R we get:

& R=2000\Omega \\\ & R=2k\Omega \\\ \end{aligned}$$ Hence, the value of R is for which $$R=2k\Omega $$ the circuit has a time constant of $$10\mu s$$. **Hence option (1) is the correct answer.** **Note:** Electricity is also found in nature in the form of lightning which occurs when large amounts of electrical energy are formed in the clouds through wind, when it occurs a large flash of electricity can be seen in the sky. Electricity travels at the speed of light. It is also a part of magnetism.