Find the current flowing through the resistance $$R$$ in the circuit shown in Fig. The internal resistances of the batteries are negligible.
Indicate the currents in all the branches using charge conservation as shown in the figure.
Applying loop rule, $$-\triangle \varphi = 0$$ in the loops $$1A781, 1B681$$ and $$B456B$$, respectively, we get
$$\xi_{0} = (i_{0} - i_{1}) R_{1} (1)$$
$$i_{3}R_{3} + i_{1}R_{2} - \xi_{0} = 0 (2)$$ and
$$(i_{1} - i_{3})R - \xi - i_{3} R_{3} = 0 (3)$$
Solving Eqs. (1), (2) and (3), we get the sought current
$$(i_{1} - i_{3}) = \dfrac {\xi (R_{2} + R_{3}) + \xi_{0}R_{3}}{R(R_{2} + R_{3}) + R_{2}R_{3}}$$.
A d.c. main supply of e.m.f. 220 V is connected across a storage battery of e.m.f 200 V through a resistance of $$1\Omega.$$ The battery terminals are connected to an external resistance 'R'. The minimum value of 'R', so that a current passes through the battery to charge it is :
In the given circuit diagram, the currents, $$I_1 = -0.3 A, I_4 = 0.8 A$$ and $$I_5 = 0.4 A$$ are flowing as shown. The currents $$I_2I_3$$ and $$I_6$$ respectively, are:
An inductor of $$2H$$ and a resistance of $$10\Omega$$ are connected in series with a battery of $$5V$$. The initial rate of change of current is
A circuit contains an ammeter, a battery of $$30\ V$$ and a resistance $$40.8$$ ohm all connected in series. If the ammeter has a coil of resistance $$480$$ ohm and as shunt of $$20$$ ohm, the reading in the ammeter will be:
Calculate I for the given circuit diagram.
In the arrangement shown in figure, the current through $$5\Omega$$ resistor is?
Calculate the current through the circuit and the potential difference across the diode shown in figure. The drift current for the diode is $$20 \mu A . $$
A circuit shown in Fig. has resistances $$R_{1} = 20\Omega$$ and $$R_{2} = 30\Omega$$. At what value of resistance $$R_{x}$$ will the thermal power generated in it be practically independent of small variations of that resistance? The voltage between the points $$A$$ and $$B$$ is supposed to be constant in this case.
Find the magnitude and direction of the current flowing through the resistance $$R$$ in the circuit shown in Fig. if the emf's of the sources are equal to $$\varepsilon_{1} = 1.5\ V$$ and $$\varepsilon_{2} = 3.7\ V$$ and the resistances are equal to $$R_{1} = 10\Omega, R_{2} = 20\Omega, R = 5.0\Omega$$. The internal resistances of the sources are negligible.
In a circuit shown in Fig. resistances $$R_{1}$$ and $$R_{2}$$ are known, as well as emf's $$\varepsilon_{1}$$ and $$\varepsilon_{2}$$. The internal resistances of the sources are negligible. At what value of the resistance $$R$$ will the thermal power generated in it be the highest? What is it equal to?