Derive laws of resistance in series so as to explain equivalent resistance of circuit ?
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ANSWER
The resistors are connected across two points in the circuit in such a way that the current flowing through each resistor is the same and only one path is available for it to flow, then the resistors are said be connected in series.\In the figure above, three resistors R
1
,R
2
and R
3
are connected in series across the points A and B. Hence, the current (I) flowing through each of the resistors is same but the total voltage of the battery is divided.If the voltage drops across V
1
,V
2
and V
3
are R
1
,R
2
and R
3
respectively then,
V=V
1
+V
2
+V
3
…………….(i)
Now, if the resistor R instead of these three resistances R
1
,R
2
and R
3
is connected in such a way that the current flowing through the circuit remains the same, then R is called equivalent resistance of the circuit.For an equivalent resistor, V=IR…………….(ii)According to Ohm’s law,
R
1
voltage drops across, V
1
=IR
1
…………..(iii)
R
2
voltage drops across, V
2
=IR
2
…………..(iv)
R
3
voltage drops across, V
3
=IR
3
…………..(v)
Adding (iii), (iv) and (v):
V
1
+V
2
+V
3
=IR
1
+IR
2
+IR
3
……(vi)Or,
V=IR=I(R
1
+R
2
+R
3
)Or,
R=R
1
+R
2
+R
3
Thus, in series connection the equivalent resistor R is equal to the sum of all the resistors connected in series.
Explanation:
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Answer:
The equivalent resistance is where the aggregate resistance connected either in parallel or series is calculated. Essentially, the circuit is designed either in Series or Parallel. Electrical resistance shows how much energy one needs when you move the charges/current through your devices.
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