Answer

Verified

436.8k+ views

**Hint:**To solve the given problem check the diagram given in the question. They have asked to find the voltage difference across the \[20K\Omega \] resistor. Consider the position of that particular resistor and remember the formula that relates the voltage, current and resistor value.

**Formula used:**

Ohm’s law,

\[{\text{V = IR}}\], here $V$= potential difference, $I$= current flows in the circuit, $R$= resistance across the resistors

Series combination of resistors: $R = {R_1} + {R_2} + .............. + {R_n}$

Parallel combination of resistors: $\dfrac{1}{R} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + .............. + \dfrac{1}{{{R_n}}}$

**Complete step by step answer:**

Given details:

\[{R_1} = 20K\Omega \] ,

\[{R_2} = 5K\Omega \],

\[{R_3} = 8K\Omega \],

\[{R_4} = 6K\Omega \],

\[\;{R_5} = 5K\Omega \],

\[V = 9V\]

From the circuit diagram, ${R_1}$ and ${R_2}$ are connected in series combination,

Therefore,

${R'} = {R_1} + {R_2}$

After substituting the resistor values in the given equation use addition to add the values as it is a series combination,

$ \Rightarrow (20 + 5)$

$ \Rightarrow 25\Omega $ and

From the circuit diagram, ${R_3}$ and ${R_4}$ are connected in series combination,

Therefore,

${R^{''}} = {R_3} + {R_4}$

After substituting the resistor values in the given equation use addition to add the values as it is a series combination,

$ \Rightarrow ({\text{8 + 6)}}$

$ \Rightarrow 14$

Again $R'$ and ${R^{''}}$ are connected in parallel combination,

Therefore, we can calculate as,

$\dfrac{1}{{{{\text{R}}^{'''}}}} = \dfrac{1}{{{{\text{R}}'}}} + \dfrac{1}{{{{\text{R}}^{''}}}}$

We can use fraction addition to add the values, we get,

$ \Rightarrow \dfrac{1}{{{{\text{R}}^{'''}}}} = \dfrac{1}{{25}} + \dfrac{1}{{14}}$

$ \Rightarrow \dfrac{1}{{{{\text{R}}^{'''}}}} = 0.04 + 0.071428$

With the help of addition again we get,

$ \Rightarrow $$\dfrac{1}{{{{\text{R}}^{'''}}}} = 0.111428$

We need ${R^{''}}$only we are taking the left-hand side numerator to the right hand side and dividing it with the $0.111428$ we get,

$ \Rightarrow {R^{'''}} = 8.97440\Omega $

Now, the current flows through the right-hand side circuit having $9V$ voltage drop can be calculated as,

${{\text{I}}'} = \dfrac{9}{{8.97440}}$

By using division, we get,

$ \Rightarrow 1.002852A$

Now, the current flows through the left-hand side circuit having $9V$ voltage drop can be calculated as,

${I^{''}} = \dfrac{9}{5}$

By using division, we get,

$ \Rightarrow 1.8A$

According to Ohm’s law $V = IR$. We have got the values for $I$and $R$ we can substitute in the formula to find the voltage.

We can calculate the voltage across \[20K\Omega \]

$ \Rightarrow V = 1.8 \times 20$

$\therefore 36V$

**The correct option is C**

**Note:**

-Fixed resistors: It has resistances that change slightly with time, temperature or operating voltage.

-Variable resistors: It can be used to adjust circuit elements (such as a volume control or a lamp dimmer), or as sensing devices for heat, humidity, light, force, or chemical activity.

-Series resistance: It is the combination of resistors connected in series.

-Parallel resistance: It is the combination of resistors connected in parallel.

-Ohm’s law: This law states that potential difference across a circuit is directly proportional to the current flows through the circuit.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

The polyarch xylem is found in case of a Monocot leaf class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Change the following sentences into negative and interrogative class 10 english CBSE

Casparian strips are present in of the root A Epiblema class 12 biology CBSE