27.6
An 18 Volt battery is used to charge a run-down battery of 2 ohm internal resistance and lights a bulb of 3 ohms. The current through the run-down battery and the bulb is 1 ampere and 2 amperes, respectively, in the shown direction.
What will be the current and internal resistance of the power supplying battery and the emf of the run-down battery?
Since there are three unknown quantities, three equations will be required.
The first equation is obtained by applying Kirchhoff's first rule at junction "a". This gives the current flowing through the power supplying battery.
The second equation is obtained by applying Kirchhoff's second rule, along the outer loop of the circuit.
Solving this expression results in the value of internal resistance of the power supplying battery.
The third equation is obtained by applying the loop rule in the left-hand loop. Solving this equation gives the emf of the run-down battery.
The negative sign indicates that the actual polarity of the battery is opposite to the assumed polarity in the circuit.
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