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19/07/2021 3:48 pm
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(a) With the help of a circuit diagram, deduce the equivalent resistance of two resistances connected in series.
(b) Two resistances are connected in series as shown in the diagram :
(i) What is the current through the 5 ohm resistance?
(ii) What is the current through R?
(iii) What is the value of R?
(iv) What is the value of V?
1 Answer
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19/07/2021 3:52 pm
(a) Fig shows two resistance R1 and R2 connected in series with a battery of V volts.
Let the p.d. across R1 is V1 and the p.d. across R2 is V2.
s.t V = V1 + V2 ......(1)
Let the equivalent resistance be R and current flowing through whole circuit is I
By Ohm's law
\(\frac{V}{I}\) = R
V = I x R .....(2)
Applying Ohm's law to both R1 and R2
V1 = I x R 1.........(3)
V2 = I x R2 ..........(4)
From eqs. (1), (2), (3) and (4), we get
I x R = I x R1 + I x R2
I x R = I x (R1 + R2)
R = R 1+ R2
(b)(i) Current through 5 ohm resistor = 10/5 = 2A
(ii) Since 5 ohm resistor and R are connected in series, so same current flows through them.
So, Current through R = 2A
(iii) V = IR
R = \(\frac{V}{I}\) = \(\frac{6}{2}\) = 3 ohm
(iv) V = 10 + 6 = 16 V