Is work dome by a battery always equal to the thermal energy develop in electrical circuits? What happens if a capacitor is connected in the circuit?

What is an electric circuit ?

A nonideal battery is connected to a resistor. Is work done by thr battery equal to the hermal energy developed in the resistor?Does your answer change If the battery is ideal?

Fuse is connected in an electric circuit.

Find total energy stored in capacitors given in the circuit

Do "work done by the battery" and "the thermal energy developed"represent two names of the same physical quantity?

For the given circuit, the total energy stored in the circuit when a 12V battery is connected.( C=10 muF )

A student in a lab took a coil and connected it to a 12 VDC source. He measures the steady state current in the circuit to be 4 A . He then replaced the 12 VDC source by a 12V,(omega=50rad//s)AC source and observes that the reading in the AC ammeter is 2.4 A . He then decides to connect a 2500 muF capacitor in series with the coil and calculate the average power developed in the circuit. Further he also decides to study the variation in current in the circuit (with the capacitor and the battery in series). The power developed in te circuit when the capcitor of 2500 muF is connected in sereis with the coil is

In an electric circuit shown alongside, find terminal voltage of the battery

An LC circuit contains a 20 mH inductor and a 50 mu F capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0. (a) What is the total energy stored initially ? Is it conserved during the oscillalions? (b) What is the natural frequency of the circuit? (c ) At what time is the energy stored? (i) Completely electrical ? (ii) Completely magnetic ? (d) At what time is the total energy shared equally between the inductor and the capacitor ? (e) If a resistor is inserted in the circuit, how much energy is eventually dissipated as heat ?

A student in a lab took a coil and connected it to a 12 VDC source. He measures the steady state current in the circuit to be 4 A . He then replaced the 12 VDC source by a 12V,(omega=50rad/s)AC source and observes that the reading in the AC ammeter is 2.4 A . He then decides to connect a 2500 muF capacitor in series with the coil and calculate the average power developed in the circuit. Further he also decides to study the variation in current in the circuit (with the capacitor and the battery in series). Which of the following graph roughly matches the variation of current in the circuit (with the coil and capacitor connected in the series) when the angulr frequency is decreased from 50 rad/s to 25 rad/s?