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Q.

Is it true that the current through the $R Ω$ resistor in the given circuit is $2 A$ ?

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a

True

b

False

answer is A.

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Detailed Solution

The above given statement is true.
In a series circuit, all components are connected end-to-end, forming a single path for current flow. From the given circuit, we can understand that the connection is in series. Thus the current through the resistors are the same while voltage across them is different.
From Ohm’s law

R = \frac{V}{I} . . . . . . . . . . . . . . . (a)

R =

Resistance

V =

Voltage

I =

Current
From (a) we can write

I = \frac{V}{R} . . . . . . . . . . (b)

Let

R_{1} = 5 Ω

and

R_{} =

unknown resistor
Let the voltage across

5 Ω

resistor is

V_{1}

and the voltage across

R Ω

resistor is

V_{2}

It is given

V_{1} = 10 V

V_{2} = 6 V

Since the circuit is connected in series,

I

is same through

R_{1}

and

R_{}

From (b)
current passing through the circuit

I_{} = \frac{V_{1}}{R_{1}} . . . . . . . . . . . . . (i)

And

I_{} = \frac{V_{2}}{R} . . . . . . . . . . . . . . (ii)

From (i) we get

I_{} = \frac{10}{5}

{= > I}_{} = 2 A

Since the resistors are connected in series, current through

5 Ω

and

R Ω

is the same.
Hence the current passing through

R Ω

resistor is

2 A

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