Question

Two circuits, one series and one parallel are made
of two resistors of resistance 2 and 3 across a
9V battery, In which combination and in which
resistor is the magnetic field the maximum?

Answer 1

Explanation:

total resistance in series=5 ohm

total resistance in parallel=6/5ohm

current in series =1.8 ampere

current in parallel=7.5ampere

therefore magnetic field will be more in parallel as compared to series

and maximum in 2ohm resistor

Answer 2

Given:

Resistance of first resistor $=\[2\Omega \]$

Resistance of second resistor $=\[3\Omega \]$

Voltage of battery $=9V$

To Find: The combination and resistor having maximum magnetic field

Solution:

In series combination:

Total resistance in series combination is given as

$\[{R_s} = {R_1} + {R_2}\]$

$\[{R_s} = 2\Omega + 3\Omega \]$

$\[{R_s} = 5\Omega$

Current in the series combination is given by

$\[I = \frac{V}{R}\]$

$\[I = \frac{{9V}}{{5\Omega }}\]$

$\[I = 1.8A\]$

In parallel combination:

Total resistance in parallel combination is given as

$\[\frac{1}{{{R_p}}} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\]$

$\[\frac{1}{{{R_p}}} = \frac{1}{{2\Omega }} + \frac{1}{{3\Omega }}\]$

$\[\frac{1}{{{R_p}}} = \frac{{3 + 2}}{6}\]$

Therefore,

$\[{R_p} = 6/5\Omega \]$

Current in the parallel combination is given by

$\[I = \frac{{9V}}{{6/5\Omega }}\]$

$I=7.5A$

Magnetic field is directly proportional to the current.

As the current in the parallel combination is more, therefore, magnetic field is maximum in parallel combination.

Also,

Current in $\[2\Omega \]$ resistor $\[ = \frac{{9V}}{{2\Omega }}\]$

Current in $\[2\Omega \]$ resistor $=4.5A$

Similarly,

Current in $\[3\Omega \]$ resistor $\[ = \frac{{9V}}{{3\Omega }}\]$

Current in $\[3\Omega \]$ resistor $=3A$

As the current in $\[{2\Omega }\]$ is more, therefore, magnetic field is maximum in $\[{2\Omega }\]$ resistor.