Question:

Five equal resistances each of resistance \(R\) are connected as shown in the figure. A battery of \(V\) volts is connected between \(A\) and \(B\). The current flowing in \(AFCEB\) will be

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Apply the concept of the Wheatstone bridge to the given circuit

Updated On: Aug 7, 2023
  • $\frac{3V}{R}$
  • $\frac{V}{R}$
  • $\frac{V}{2R}$
  • $\frac{2V}{R}$
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The Correct Option is C

Approach Solution - 1

By rearranging the given figure, we obtained an equivalent circuit shown in the figure below

Since the ratio of the resistance of the arms FC to CE is equal to the ratio of the resistance of arms FD to DE, therefore the given figure represents a Wheatstone Bridge. 

 

According to the principle of Wheatstone Bridge, if FC/CE = FD/DE then no current will flow through the arm CD.

Therefore, the equivalent circuit can be given by

Now, the equivalent resistance of AFCEB, R1 = R + R = 2R

Also, the equivalent resistance of AFDEB, R2 = R + R = 2R

The equivalent resistance of the circuit, 1/Req = 1/R1 +1/R2 = 1/2R + 1/2R = 1/R

⇒ Req = R

From Ohm's law, the total current flowing through the branch AFCEB, I = Total voltage/Total resistance

⇒  I = V/2R

Hence, when five equal resistances each of resistance R are connected as shown in the figure. A battery of V volts is connected between a and b. the current flowing in AFCEB will be V/2R.

Discover More from Chapter: Current Electricity

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Approach Solution -2

The Correct Answer is (C): \(\frac{V}{2R}\)

Real Life Applications 

1. Electrical appliances like irons, hair dryers, etc. all have resistors to control the current flow. 

Electric Press
2. The filament in a light bulb has a high resistance in the form of filament. 

Bulb Filament Graph
3. Circuit breakers: Circuit breakers have small resistor that melts if the current flow through them is too high. 
4. Diodes have resistance to current flow in one direction. 

Question can also be asked as 

1. What is the current flowing through branch AFCEB in the circuit shown? 
2. What is the current flowing through resistor R in the circuit shown? 
3. What is the current flowing through the Wheatstone bridge in the circuit shown?

 

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Approach Solution -3

The Correct Answer is (C): \(\frac{V}{2R}\)

Wheatstone Bridge

  • Wheatstone Bridge is an arrangement of four resistors in the form of a bridge used for measuring one unknown resistor in terms of other three known resistors.

Principle of Wheatstone Bridge

  • A Wheatstone Bridge works on the principle of null deflection or zero deflection.
  • If the ratio of P to Q is equal to the ratio of R to S, then no current will flow through the galvanometer.
  • In this case, the Wheatstone Bridge is said to be balanced.
  • If P/Q = R/S, then Ig = 0

Wheatstone Bridge Formula

  • The formula of the Wheatstone Bridge is given by

R = PS/Q

Where

  • R is the unknown resistance
  • S is the standard arm of the bridge
  • P and Q is the ratio of the arm of the bridge
Related Topics
Resistors in Series and Parallel CombinationCircuit DiagramResistor Colour Codes
Carbon ResistorCombination of Cells in Series and in ParallelUnit of Current
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Concepts Used:

Current Electricity

Current electricity is defined as the flow of electrons from one section of the circuit to another.

Types of Current Electricity

There are two types of current electricity as follows:

Direct Current

The current electricity whose direction remains the same is known as direct current. Direct current is defined by the constant flow of electrons from a region of high electron density to a region of low electron density. DC is used in many household appliances and applications that involve a battery.

Alternating Current

The current electricity that is bidirectional and keeps changing the direction of the charge flow is known as alternating current. The bi-directionality is caused by a sinusoidally varying current and voltage that reverses directions, creating a periodic back-and-forth motion for the current. The electrical outlets at our homes and industries are supplied with alternating current.