Question

(b)
Two resistors X and Y of resistances 2 and 3 respectively are
first joined in parallel and then in series. In each case the voltage
supplied is 5 V.
(1) Draw circuit diagrams to show the combination of resistors
in each case.
Calculate the voltage across the 3 ohm resistor in the series
combination of resistors.​

Answer 1

Answer:

Explanation: it is given in the picture

Answer 2

(1) The equivalent resistance of series combination is 5 $\Omega$

The equivalent resistance of series combination is 1.2 $\Omega$

(2)  The voltage across 3 ohm resistor in series combination is 3 ohm

Explanation:

Given as :

The resistance value of resistor x = $R_1$ = 2 ohm

The resistance value of resistor y = $R_2$ = 3 ohm

The supply voltage = V = 5 v

According to question

(1) The series and parallel combination as shown in figure

For series combination of two Resistor

$R_e_q$  = $R_1$  +  $R_2$

i.e  $R_e_q$ = 2 $\Omega$ + 3 $\Omega$

∴   $R_e_q$ = 5 $\Omega$

So, The equivalent resistance of series combination =  $R_e_q$ = 5 $\Omega$

For Parallel combination of two Resistor

$\dfrac{1}{R_e_q}$  = $\dfrac{1}{R_1}$ + $\dfrac{1}{R_2}$

i.e $\dfrac{1}{R_e_q}$  = $\dfrac{1}{2}$ + $\dfrac{1}{3}$

Or, $\dfrac{1}{R_e_q}$   = $\dfrac{2+3}{6}$

Or, $\dfrac{1}{R_e_q}$  = $\dfrac{5}{6}$

∴  $R_e_q$ = $\dfrac{6}{5}$

i.e   $R_e_q$ = 1.2 $\Omega$

So, The equivalent resistance of parallel combination =  $R_e_q$ = 1.2 $\Omega$

Hence,  The equivalent resistance of series combination is 5 $\Omega$

The equivalent resistance of series combination is 1.2 $\Omega$   Answer

(2) The voltage across the 3 ohm resistor in series combination of Resistor

Let The voltage = v volt

The supply voltage = V = 5 volts

∵ Equivalent resistance in series combination = $R_e_q$ = 5 ohm

Let The amount of current flow in circuit = I  amp

∵ current = $\dfrac{voltage}{equivalent resistance}$

∴             I = $\dfrac{V}{R_e_q}$

Or,          I = $\dfrac{5 volt}{5 ohm}$

i.e           I = 1 amp

So, The flow of current in circuit =   I = 1 amp

As current in series circuit is same through each resistor

So, Current through 3 ohm resistor = I = 1 amp

Therefore voltage across 3 ohm resistor = current × resistance

i,e  $v_3$ = I × $R_3$

∴   $v_3$ = 1 amp × 3 ohm

Or, $v_3$ = 3 volt

So, The voltage across 3 ohm resistor = $v_3$ = 3 ohm

Hence, The voltage across 3 ohm resistor is 3 ohm  Answer