How you would connect three resistors each of resistence of 18ohm and 2ohm
Answers
Answer:
To obtain a combined resistance of 9 ohms, three resistors each of resistance 6 ohm should be connected in a parallel circuit and one in series.
In a parallel circuit, the equivalent resistance of all the resistors connected is equal to the reciprocal value of the sum of the individual resistances.
In a series circuit, the equivalent resistance of all the resistors connected is equal to the sum of the resistance values of each of the individual resistor.
So in a parallel circuit, total resistance = \frac{1}{Rt}=\frac{1}{R 1}+\frac{1}{R 2}+\frac{1}{R 3}
Rt
1
=
R1
1
+
R2
1
+
R3
1
or
R t= \frac{\frac{1}{2}}{R 1}+\frac{1}{R 2}+\frac{1}{R 3}
R1
2
1
+
R2
1
+
R3
1
.
In a series circuit, total resistance = R1 +R2 + R3
(i) To get 9 ohms, two resistors should be connected in parallel and one in series.
So,
Rt in parallel will be
Rt = \frac{1}{\frac{1}{\mathrm{R}_{1}}+\frac{1}{\mathrm{R}_{2}}}=\frac{1}{\frac{1}{6}+\frac{1}{6}}
R
1
1
+
R
2
1
1
=
6
1
+
6
1
1
= 3 ohms
One resistor is connected in series with the 3 ohms, so
Rt in series will be Rt = R1 +R2 = 6+3 = 9 ohms
(ii) To obtain a combined resistance of 4 ohms, two resistors (of 6 ohms each) are connected in series and one in parallel to the series.
So,
Rt in series = R1 +R2 = 6+6 = 12 ohms
Rt in parallel = \frac{1}{R t}=\frac{1}{R 1}+\frac{1}{R 2}=\frac{1}{6}+\frac{1}{12}
Rt
1
=
R1
1
+
R2
1
=
6
1
+
12
1
= 4 Ohms