Question

the current in a circuit with an external resistance of 3.75ohm is 0.5 A. When a resistance of 1ohm is introduced into the the circuit , the current becomes 0.4A. The emf of the power source​

Answer 1

hope u understand the answer

Answer 2

The emf of the power source​ is 2.0 V.

Explanation:

Given that,

External resistance = 3.75 ohm

Current =0.5 A

Resistance = 1 ohm

New current = 0.4 A

We need to calculate the emf of the power source

Using formula of emf for current

$I=\dfrac{E}{r+R}$

Put the value into the formula

$0.5=\dfrac{E}{r+3.75}$

$E=0.5(r+3.75)$....(I)

Now for new current

$I'=\dfrac{E}{r+(R+1)}$

Put the value into the formula

$0.4=\dfrac{E}{r+4.75}$

$E=0.4(r+4.75)$....(II)

From equation (I) and (II)

$0.4(r+4.75)=0.5(r+3.75)$

$0.4r+0.4\times4.75=0.5r+0.5\times3.75$

$0.4\times4.75-0.5\times3.75=0.5r-0.4r$

$0.025=0.1r$

$r=\dfrac{0.025}{0.1}$

$r=0.25$

Put the value in equation (I)

$0.5=\dfrac{E}{0.25+3.75}$

$0.5=\dfrac{E}{4}$

$E=2.0\ V$

Hence, The emf of the power source​ is 2.0 V.

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