"... find the value of x so that the ***external power *** supplied by the battery remain the same..."
We know that maximum power will be supplied to the external load RL when RL = internal resistance = 5 ohms.
I interpret this question to mean "Find two sub-optimal values for RL, one greater than 5 ohms {=x}
and one less than 5 ohms {formed by x in parallel with 6 ohms} such that the power dissipated in (x) and (x // 6) is the same."
I suggest RL = x = 7.5 ohms fits the bill, dissipating 19.2 W.
7.5 ohms in parallel with 6 ohms gives RL = 3.3333 ohms, also dissipating 19.2 W in the parallel pair
Remains the same as what? The power supplied with x ohms load only? Adding any resistor in parallel (and you do say the 6 ohms is across the battery, ie, in parallel) will always increase the power.
So this is impossible as listed and cannot be answered.
Unless the connects are not as you list. Perhaps X and the 6Ω are in series, not in parallel? But in this case the 6Ω will decrease the power.
Assuming the 6 ohms is put in parallel with x;
It is impossible to keep the power supplied by the battery the same by increasing the load.
If the 6 ohms is put in series with x then the value x must be reduced by 6 to maintain the same power supplied by the battery. If x is greater than 6 ohms, there is no solution.
it is possible only when the resistor x=0. it means that you have short circuit the battery terminal and current through the loop is 20/5 = 4A. and whole power is dissipated in battery itsself and the internal resistor.
now if you add a resistor of any ohm( say 6 ohm ) value across the battery the current will follow the low resistive path . now the teminals are shorted , no current will flow through 6 ohm resistor.
and current will remain same i.e 4A. and power dissipation remains same ( ofcourse of no use.)
other case is if x is other than zero . it is not possible that power dissipation remains same . because both resistor are in parallel and both will contribute to power dissipation.
given the 20volts battery an internal resistance of 5 ohms is connected to a resistor of x ohms. if an additional 6 ohms is connected across the battery, find the value of x so that the external power supplied by the battery remain the same?
