Question

how can you connect 4 resistors of 3 ohms so as to get a net resistance of 3 ohms​

Answer 1

Need to FinD:-

• How can you connect 4 resistors of 3 Ω so as to get a net resistance of 3 Ω .

$\red{\frak{Given}}\Bigg\{ \sf Four \ Resistances \ of \ 3 \Omega.$

For getting a net resistance of 3Ω , we will connect two 3Ω resistance in series . We will similarly connect the other two in series . Lastly we will connect the above two combinations in parallel.

Calculation of net Resistance,

• Since the two Resistances are connected in series , the net resistance will be ,

$\sf\longrightarrow R_{net}= R_1 + R_2 \\\\\\\sf\longrightarrow R_{net}= 3\Omega + 3\Omega \\\\\\\sf\longrightarrow \underline{\underline{\red{R_{net}= 6\Omega }}}$

• Similarly the net resistance of the two resistors connected in series will be 6 Ω .

• Now they are connected in parallel this means to 6 ohm resistors are connected in parallel . So that the network distance will be ,

$\sf\longrightarrow R_{net}= \dfrac{R_1 R_2}{R_1+R_2} \\\\\\\sf\longrightarrow R_{net}= \dfrac{ 6*6\Omega^2}{(6+6)\Omega } \\\\\\\sf\longrightarrow R_{net}= \dfrac{ 36\Omega^2}{12\Omega } \\\\\\\sf\longrightarrow \underline{\underline{\red{R_{net}= 3\Omega }}}$

Hence we got the net resistance as 3Ω.